395 Sentences With "well ordered" | Random Sentence Generator

People who live in messy homes lead messy lives, while people who live in well-ordered homes lead well-ordered ones.

Alternatively, the natural world is seen in the form of the gardens of the institution where he had been incarcerated — well-ordered nature intended to cultivate a well-ordered mind.

Eurobank is an interesting takeover subject, with a well-ordered business.

If it were really this well ordered, I'd never get anything done.

Genet's writings uncover the perverse anarchies that operate within well-ordered hierarchies.

As in Dus, the dwellings were simple, built of sticks and grass, and well ordered.

Communist Party officials tout it as evidence of a well-ordered rhythm in their country's politics.

To computer scientists, "algorithm" means a well-ordered set of steps to achieve a particular goal.

And everything trades in a well-ordered fashion," David Kostin told CNBC's "Squawk on the Street.

Only in relation to our imagination can things be called beautiful or ugly, well-ordered or confused.

As if understanding that, this store, in the back, sells other accouterments of a well-ordered life.

In reality of course, governments strongly regulate financial securities to ensure that those exchanges are well-ordered.

I'm like many of my associates; I find solace in the well-ordered setting of the laboratory.

Reactionary stories always begin with a happy, well-ordered state where people willingly shared a common destiny.

The film bounces around, with connections between topics that feel more fibrous than a well-ordered shot list.

But today there are few less piratical places on earth than this tidy and well-ordered little island.

But an affordable college education, though perhaps not a wonder, is a necessity for a well-ordered society.

On those, he used simpler chords and riffs to build understated, well-ordered grooves and a coolly Afrocentric sound.

Early-modern European naturalists peered into termite mounds, anthills, and beehives and saw microcosms of well-ordered states: monarchs, soldiers, laborers.

The suburbs of Europe and North America, with their well-ordered streets and parks, increasingly seem like exceptions to the global rule.

Back by the boat I encountered a man with his entire chest and stomach covered in the well-ordered markings of scarification.

It captures the unease of the central character within seemingly well-ordered Japan that the review suggests the crime novel conveys so well.

It was Ron Sahadi who assumed his father's usual post on that blustery Saturday, standing by the registers, observing the well-ordered throng, telling stories.

My third daughter was born, on a bright and chilly December day, facing a life of uncertainty that threatened to rock my well-ordered existence.

The Sidama referendum was a peaceful and mostly well-ordered affair (though there were allegations of voter fraud in the weeks leading up to it).

Heller established an individual's right to keep a gun in the home, outside the context of the "well-ordered militia" stipulated in the Second Amendment.

It sounds like a lot, but in practice what you get is a well-ordered list of the stuff you need, easily acted upon right there.

Humes's tireless curation of figure and fact, his well-reasoned arguments and his uncluttered, well-ordered prose may turn the ship that's just begun to budge.

Into her well-ordered, meticulously moneyed world bursts Penny Rust, an Aussie who is as free-form and fun-loving as Josephine is calculated and cunning.

She presents the setting as a fantastical place, as well-ordered as clockwork, and seems to delight in depicting all the moving parts of this world.

Individuals were encouraged to think of themselves as examples of more general and generic models of human beings, who, taken together, made up a well-ordered social whole.

The most striking thing was how well ordered the whitewashed villages were and how every possible piece of arable land — even steep hillsides — had been plowed and planted.

With its well-ordered gridiron layout and comfortable hillside homes, the village offered its residents the chance of a new life away from the hustle and bustle of the city.

The gargantuan yet well-ordered text brims with lucid annotations, extended quotations from rare source materials, fascinating paraphrases, provocative formulations and philosophical propositions, poetic digressions, lyrical aphorisms and experimental theses.

The bloodshed sent this well-ordered, Baroque city into a panic, as the authorities declared a state of emergency and halted public transportation in the middle of the rush-hour commute.

On a well-ordered desk, a legal pad topped by a ruler and a pencil sits near the small device with which the artist measured his oxygen level throughout the day.

If the story were linear and well-ordered, coming in on the third season would be like entering a really convoluted play for the third act, which is always a bad idea.

FOR A striking example of how far-right parties can change the politics of a democratic Western country, even without ever holding office, look no further than to wealthy, well-ordered Denmark.

The idea of a challenging yet well-ordered world so prevalent in modernist literature may seem dated now, but as a young reader and video game player I found it tremendously appealing.

We request upon you to join with many other political and religious leaders to proclaim with one voice that the "alt-right" is racist, evil, and antithetical to a well-ordered, peaceful society.

This shows that, for many Muslims, the revealed truths of Islam are not only a matter of personal conviction but must also have a central place in the public sphere of a well-ordered society.

Three thousand persons were present, and the well-ordered and scientific pummelling was in full swing when a force of military and police, acting under the orders of the recruiting authorities, took possession of the building.

"The US Refugee Admissions Program employs teams of highly-trained DHS officers who travel overseas to interview and screen each individual applicant for refugee admission in a process that is comprehensive, well-ordered and highly deliberative," he said.

So I often retreat, my mind escaping the room where I learn to mimic emotion, returning itself to some well-ordered facts absorbed from a musty book, its scent still lingering on my fingers, a source of comfort.

As he covers the group's contentious but remarkably well-ordered meetings, his movie feels like a documentary about AIDS in the early 1990s, and the different angles of attack different groups brought to bear on the health crisis in France.

My vision of the maximally free, anarcho-capitalist society seemed to me an indispensable guiding light, a compass by which to steer a course through the rugged landscape of real-world politics toward the promised land — the ideally good and morally well-ordered society.

The relationship they form is rich and complicated, but Anderson builds it around their idiosyncrasies and their stubbornness, and once it becomes clear how set both of them are in their ways, the story lays out endless possibilities for how their well-ordered world can fall apart.

This depiction of Christian domesticity, with male heads of household shaping spiritual matters for their female counterparts, is central to the film's vision of a "good" Christian life: a chain of well-ordered relationships in which wives submit to their husbands, and husbands submit to Trump.

While we may now read Casta Painting negatively, as a record of programed exclusion, it was intended to convey what was then considered a positive message, to advertise New Spain as a good place to be: racially mixed but, thanks to thorough policing, well-ordered and danger free.

The ultimate political teaching of Adams's deeply political epic, then, is an unfashionable optimism about the ends of politics — in which the genuinely good society, the well-ordered regime, is not a utopia but a live possibility, a hard thing to find but one worth going out to seek.

I hear what you're saying about individual rights, though I think that the first phrase about a "well ordered militia" is often ignored by the right and a case could be made that it calls into question whether or not the amendment supports individual gun ownership separately from participation in a formal (recognized?) defensive body.

" He is, Shaw writes in his preface, one of those "poor devils" who became rich "by placing their personal interests before those of the country" and thus proved "not only that they were useless for public work, but that in a well-ordered nation they would never have been allowed to control private enterprise.

Now that Abadi has met Trump, he should invite him to visit Iraq and see a city such as Sulaimani which is, by regional standards, a safe and well-ordered city of smooth highways and modern apartment blocks ringed by snow-capped mountains that feels a lot freer and more open than much of the rest of the Middle East.

ANNOUNCES KAREN HOGUET, CHIEF FINANCIAL OFFICER, TO RETIRE FEBRUARY 2019 * HOGUET WILL CONTINUE IN HER ROLE AS CFO UNTIL HER SUCCESSOR IS APPOINTED * EXTERNAL SEARCH IS UNDERWAY FOR HOGUET'S REPLACEMENT AND COMPANY ANTICIPATES A WELL-ORDERED TRANSITION * HOGUET WILL THEN REMAIN IN AN ADVISORY ROLE TO SUPPORT COMPANY DURING A TRANSITION PERIOD UNTIL FEBRUARY 2, 2019 Source text for Eikon: Further company coverage:

The original Greek word was dikaiosyne, literally just-ness, and that too has both a narrow and much wider meaning; it could refer to judicial proceedings but it is also used to render the Hebrew term tsedaqah, which describes fair, righteous, well-ordered behaviour, leading ultimately to a state of shalom, in other words peace, wholeness or the original state of creation.

Hajdu favors well-ordered statements over half-mad village-square pronouncements, and I wouldn't be surprised if the sanity of his approach had something to do with his having come of age in the wake of pioneering rock critics like Paul Williams, Robert Christgau, Greil Marcus, Richard Goldstein, Ellen Willis, Nick Tosches and Lester Bangs, all of whom made their names in the 1960s and '70s and three of whom will make you tear your hair out, despite their obvious intellect, talent, chops, élan, etc.

The values of -tuples of parameters are well-ordered by the product ordering. The formulas with parameters are well-ordered by the ordered sum (by Gödel numbers) of well-orderings. And is well-ordered by the ordered sum (indexed by ) of the orderings on . Notice that this well-ordering can be defined within itself by a formula of set theory with no parameters, only the free-variables and .

Proof of equivalence: If a set is well-ordered, then its cardinality is an aleph since the alephs are the cardinals of well-ordered sets. If a set's cardinality is an aleph, then it can be well-ordered since there is a one-to-one correspondence between it and the well-ordered set defining the aleph. First, he defined two types of multiplicities: consistent multiplicities (sets) and inconsistent multiplicities (absolutely infinite multiplicities). Next he assumed that the ordinals form a set, proved that this leads to a contradiction, and concluded that the ordinals form an inconsistent multiplicity.

The distinction between strict and non-strict well orders is often ignored since they are easily interconvertible. Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set. The well-ordering theorem, which is equivalent to the axiom of choice, states that every set can be well ordered. If a set is well ordered (or even if it merely admits a well-founded relation), the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set.

The proof starts by proving by contradiction that Ord, the class of all ordinals, is a proper class. Assume that Ord is a set. Since it is transitive set that is well-ordered by ∈, it is an ordinal. So Ord ∈ Ord, which contradicts Ord being well-ordered by ∈.

The options available at Key Stage 4 are extensive. The college is well ordered and behaviour is good.

This set is manifestly closed under well-ordered unions, but without AC it cannot be proved equal to the ∞-Borel sets (as defined in the previous section). Specifically, it is instead the closure of the ∞-Borel sets under all well-ordered unions, even those for which a choice of codes cannot be made.

Provided there exists an order isomorphism between two well-ordered sets, the order isomorphism is unique: this makes it quite justifiable to consider the two sets as essentially identical, and to seek a "canonical" representative of the isomorphism type (class). This is exactly what the ordinals provide, and it also provides a canonical labeling of the elements of any well-ordered set. Every well-ordered set (S,<) is order-isomorphic to the set of ordinals less than one specific ordinal number under their natural ordering. This canonical set is the order type of (S,<).

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. The set S together with the well-order relation is then called a well-ordered set. In some academic articles and textbooks these terms are instead written as wellorder, wellordered, and wellordering or well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element.

The rank among well-ordered sets is expressed by an ordinal number; for the natural numbers, this is denoted as (omega).

The valuation ring then consists of the finite surreal numbers (numbers with a real and/or an infinitesimal part). The reason for the sign inversion is that the exponents in the Conway normal form constitute a reverse well-ordered set, whereas Hahn series are formulated in terms of (non-reversed) well-ordered subsets of the value group.

In mathematics, the mex of a subset of a well-ordered set is the smallest value from the whole set that does not belong to the subset. That is, it is the minimum value of the complement set. The name "mex" is shorthand for "minimum excluded" value. Beyond sets, subclasses of well-ordered classes have minimum excluded values.

It is not true that the set of all finite words is well-ordered; for example, the set has no least element.

These cells form a well ordered, isolatable BB that is morphologically and compositionally comparable to those from the proximal tubule epithelial cell.

Thus Rawls considers how a "well ordered" people (liberal or decent) should behave towards outlaw or burdened societies that cannot be considered decent.

Since every infinite well-ordered set is Dedekind-infinite, and since the AC is equivalent to the well-ordering theorem stating that every set can be well- ordered, clearly the general AC implies that every infinite set is Dedekind- infinite. However, the equivalence of the two definitions is much weaker than the full strength of AC. In particular, there exists a model of ZF in which there exists an infinite set with no countably infinite subset. Hence, in this model, there exists an infinite, Dedekind-finite set. By the above, such a set cannot be well-ordered in this model.

The observation that the natural numbers are well ordered by the usual less-than relation is commonly called the well-ordering principle (for natural numbers).

Three well- orderings on the set of natural numbers with distinct order types (top to bottom): \omega, \omega+5, and \omega+\omega. Every well-ordered set is order- equivalent to exactly one ordinal number. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified with the corresponding ordinal. For example, the order type of the natural numbers is .

Cantor believed that every set could be well-ordered, but was unable to produce a proof for this result, leaving it as an open problem in 1895 (Katz 1998, p. 807).

In a well-ordered set, every non-empty subset contains a distinct smallest element. Given the axiom of dependent choice, this is equivalent to saying that the set is totally ordered and there is no infinite decreasing sequence (the latter being easier to visualize). In practice, the importance of well-ordering is justified by the possibility of applying transfinite induction, which says, essentially, that any property that passes on from the predecessors of an element to that element itself must be true of all elements (of the given well-ordered set). If the states of a computation (computer program or game) can be well-ordered—in such a way that each step is followed by a "lower" step—then the computation will terminate.

The functions from a well-ordered set to a totally ordered set may be identified with sequences indexed by of elements of . They can thus be ordered by the lexicographical order, and for two such functions and , the lexicographical order is thus determined by their values for the smallest such that . If is also well- ordered and is finite, then the resulting order is a well-order. As shown above, if is infinite this is not the case.

Surface states originating from clean and well ordered surfaces are usually called intrinsic. These states include states originating from reconstructed surfaces, where the two-dimensional translational symmetry gives rise to the band structure in the k space of the surface. Extrinsic surface states are usually defined as states not originating from a clean and well ordered surface. Surfaces that fit into the category extrinsic are: #Surfaces with defects, where the translational symmetry of the surface is broken.

1978 An instrument dedicated to performing such powder measurements is called a powder diffractometer. Powder diffraction stands in contrast to single crystal diffraction techniques, which work best with a single, well-ordered crystal.

Archbishop William Laud Regardless of religious doctrine or political belief, the vast majority in all three kingdoms believed a 'well-ordered' monarchy was divinely mandated. They disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Episcopalians generally supported a church governed by bishops, appointed by, and answerable to, the king; Puritans believed he was answerable to the leaders of the church, appointed by their congregations. The Caroline period was one of intense debate over religious practice and liturgy.

Artistic expression clarifies turbulent emotions. The process is essentially the same in scientists and philosophers as well as those conventionally defined as artists. Aesthetic quality will adhere to all modes of production in a well- ordered society.

This generalized lexicographical order is a total order if each factor set is totally ordered. Unlike the finite case, an infinite product of well-orders is not necessarily well-ordered by the lexicographical order. For instance, the set of countably infinite binary sequences (by definition, the set of functions from non-negative integers to }, also known as the Cantor space ) is not well-ordered; the subset of sequences that have precisely one (i.e. }) does not have a least element under the lexicographical order induced by , because is an infinite descending chain.

Contrary to Cantor, presently the majority of mathematicians considers undefinable numbers not as absurdities. This assumption leads, according to Kőnig, Kőnig's conclusion is not stringent. His argument does not rule out the possibility that the continuum can be well-ordered; rather, it rules out the conjunction of "the continuum can be well-ordered by a definition in language L" and "the property of being definable in language L is itself definable in language L". The latter is no longer generally held to be true. For an explanation compare Richard's paradox.

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn's lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also ). Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem.

A tree is a partially ordered set (poset) (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. In particular, each well-ordered set (T, <) is a tree. For each t ∈ T, the order type of {s ∈ T : s < t} is called the height of t (denoted ht(t, T)). The height of T itself is the least ordinal greater than the height of each element of T. A root of a tree T is an element of height 0.

Agricultural activity existed in New England before European settlers arrived in the region. By the time colonizers arrived, "Native American agriculture in southern New England had developed into a well-ordered system".Agriculture in New England. George Christie.

Bullard, Thomas E. "The Well-Ordered Abduction: Pattern or Mirage?" In: Pritchard, Andrea & Pritchard, David E. & Mack, John E. & Kasey, Pam & Yapp, Claudia. Alien Discussions: Proceedings of the Abduction Study Conference. Cambridge: North Cambridge Press. pp. 81–82.

"The Tinguian; Social, Religious, and Economic life of a Philippine tribe". Field Museum of Natural History: Anthropological Series. 14 (2): 235–493Gregorio F. Zaide (2017). "Filipinos Before the Spanish Conquest Possessed a Well-Ordered and Well- Thought-Out Religion".

"The Tinguian; Social, Religious, and Economic life of a Philippine tribe". Field Museum of Natural History: Anthropological Series. 14 (2): 235–493Gregorio F. Zaide (2017). "Filipinos Before the Spanish Conquest Possessed a Well-Ordered and Well-Thought-Out Religion".

A lawful evil character sees a well-ordered system as being easier to exploit than to necessarily follow. Examples of this alignment include tyrants, devils, corrupt officials, undiscriminating mercenary types who have a strict code of conduct, blue dragons, and hobgoblins.

These materials have been shown to exhibit a variety of different phases ranging from well ordered patterns to chaotic states (see below). Recent experimental investigations have suggested that the various dynamical phases exhibited by active fluids may have important technological applications.

International law after World War II establishes the principle of sovereign equality, and therefore to subject a sovereign state to outside intervention is generally considered illegal. To deal with this potential conflict between humanitarian intervention and the international legal system, there are some philosophical attempts to conciliate the two concepts and specify conditions for ethically justified interventions. John Rawls, one of the most influential political philosophers of the twentieth century, offers his theory of humanitarian intervention based on the notion of "well-ordered society." According to Rawls, a well-ordered society should be peaceful and legitimate, and it must respect basic human rights.

The Protestant Reformation created a Church of Scotland, or 'kirk', Presbyterian in structure, and Calvinist in doctrine. Presbyterian churches were ruled by Elders, nominated by congregations; Episcopalian were governed by bishops, appointed by the monarch. In 1584, bishops were imposed on the kirk against considerable resistance; since they also sat in Parliament and usually supported Royal policies, arguments over their role were as much about politics as religion. The vast majority of Scots, whether Covenanter or Royalist, believed a 'well- ordered' monarchy was divinely mandated; they disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs.

Denzil Holles, a leader of the Presbyterian faction in Parliament When the First English Civil War began in 1642, all parties agreed a 'well-ordered' monarchy was divinely mandated. They disagreed on what 'well-ordered' meant, particularly the balance of power between king and Parliament, and who held ultimate authority in clerical affairs. There was considerable alignment among moderates, choice of sides often being down to personal loyalties and relationships. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; Parliamentarians believed he was answerable to the leaders of the church, appointed by their congregations.

Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set. The position of each element within the ordered set is also given by an ordinal number. In the case of a finite set, the basic operation of counting, to find the ordinal number of a particular object, or to find the object with a particular ordinal number, corresponds to assigning ordinal numbers one by one to the objects. The size (number of elements, cardinal number) of a finite set is equal to the order type.

Whereas the notion of cardinal number is associated with a set with no particular structure on it, the ordinals are intimately linked with the special kind of sets that are called well-ordered (so intimately linked, in fact, that some mathematicians make no distinction between the two concepts). A well-ordered set is a totally ordered set (given any two elements one defines a smaller and a larger one in a coherent way), in which every non- empty subset of the set has a least element. In particular, there is no infinite decreasing sequence. (However, there may be infinite increasing sequences.) Ordinals may be used to label the elements of any given well- ordered set (the smallest element being labelled 0, the one after that 1, the next one 2, "and so on"), and to measure the "length" of the whole set by the least ordinal that is not a label for an element of the set.

Transfinite numbers: Numbers that are greater than any natural number. Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: Nilpotent numbers.

Each ordinal associates with one cardinal, its cardinality. If there is a bijection between two ordinals (e.g. and ), then they associate with the same cardinal. Any well-ordered set having an ordinal as its order-type has the same cardinality as that ordinal.

An outline of the general proof and the criteria can be found in James Munkres' Topology. However, a specific case (domain is restricted to the positive integers instead of any well-ordered set) of the general recursive definition will be given below.

The Berlin copy is especially carefully executed. The helmet is cocked back, with short curly hair bursting out at the temples. The beard is tightly cropped with many small, well-ordered curls. Broad, even eyelids ring the eyes and eyebrows are carved above.

However, unlike Plato, he believed that achieving a well-ordered soul had a higher purpose: living in accordance with God's commands. His view of morality was thus heteronomous, as he believed in deference to a higher authority (God), rather than acting autonomously.

Charles I; by 1648, a significant element felt only his death could end the conflict When the First English Civil War began in 1642, the vast majority on both sides believed a 'well-ordered' monarchy was divinely mandated. They disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; Puritans believed he was answerable to the leaders of the church, appointed by their congregations. However, 'Puritan' was a term for anyone who wanted to reform, or 'purify', the Church of England, and contained many different perspectives.

When an enumeration is used in an ordered list context, we impose some sort of ordering structure requirement on the index set. While we can make the requirements on the ordering quite lax in order to allow for great generality, the most natural and common prerequisite is that the index set be well-ordered. According to this characterization, an ordered enumeration is defined to be a surjection (an onto relationship) with a well-ordered domain. This definition is natural in the sense that a given well-ordering on the index set provides a unique way to list the next element given a partial enumeration.

Although the vast majority believed a 'well-ordered' monarchy was a divinely mandated requirement, they disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; most Parliamentarians were Puritans, who believed he was answerable to the leaders of the church, appointed by their congregations. However, Puritan meant anyone who wanted to reform, or 'purify', the Church of England, and contained many different opinions. Some simply objected to Laud's reforms; Presbyterians like Pym wanted to reform the Church of England, along the same lines as the Church of Scotland.

Charles I; by 1648, a significant element felt only his death could end the conflict When the First English Civil War began in 1642, the vast majority on both sides believed a 'well-ordered' monarchy was divinely mandated. They disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; Puritans believed he was answerable to the leaders of the church, appointed by their congregations. However, 'Puritan' was a term for anyone who wanted to reform, or 'purify', the Church of England, and contained many different perspectives.

Among the most significant achievements of Syedna Ismail Badruddin’s reign was a renaissance in Dawat knowledge. When Syedna Badruddin became Dai, he established a well-ordered institution of learning in Jamnagar. Students came from far and wide. Syedna Badruddin himself taught these students many Dawat books.

Since the possible values of are well-ordered, this property can be established by proving that for any with minimal value of in its class. Note that, for a Euclidean function that is so established, there need not exist an effective method to determine and in (EF1).

The region of Bethioua is known for its population of Berber origin which bears the name of the place. The official construction of the village according to the well-ordered rectangular plans of the time dates back to 1883, but will soon overflow its original framework.

For example, the even and odd natural numbers form disjoint cofinal subsets of the set of all natural numbers. If a partially ordered set A admits a totally ordered cofinal subset, then we can find a subset B that is well-ordered and cofinal in A.

Given an array of objects taken from a well-ordered set (such as numbers), the range minimum query (with ) returns the position of the minimal element in the specified sub-array . For example, when , then the answer to the range minimum query for the sub-array is , as .

The complexity of a generalized Heegaard splitting is the multi-set {c(S_i)}, where the index runs over the Heegaard surfaces in the generalized splitting. These multi-sets can be well-ordered by lexicographical ordering (monotonically decreasing). A generalized Heegaard splitting is thin if its complexity is minimal.

For an infinite set the order type determines the cardinality, but not conversely: well-ordered sets of a particular cardinality can have many different order types, see Section #Natural numbers for a simple example. For a countably infinite set, the set of possible order types is even uncountable.

Thus it follows that together with the above ordering is an ordered ring. The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered.. This is equivalent to the statement that any Noetherian valuation ring is either a field—or a discrete valuation ring.

Pym and Hampden were among the few to understand only military victory could compel Charles to keep his commitments. He openly told foreign ambassadors any concessions were temporary, and would be retrieved by force if needed, an approach confirmed by the Scottish experience. The Irish Catholic rebels claimed approval for their actions; while untrue, the assertion was given weight by his attempts to use Irish troops against the Scots, and initial refusal to condemn the rebellion. However, regardless of religion or political belief, in 1642 the vast majority believed a 'well-ordered' monarchy was divinely mandated; where they disagreed was what 'well-ordered' meant, and who held ultimate authority in clerical affairs.

Archbishop Laud, whose reforms led to increasing opposition to the role of bishops In 1642, the vast majority of Englishmen were 'Royalist', in the sense of a shared belief that a 'well-ordered' monarchy was divinely mandated. They disagreed on what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; Parliamentarians, many of whom were Puritans, believed he was answerable to the leaders or Elders of the church, appointed by their congregations. "Puritan" was a term for anyone who wanted to reform, or 'purify', the Church of England, and contained many different sects.

Every element s of a well-ordered set, except a possible greatest element, has a unique successor (next element), namely the least element of the subset of all elements greater than s. There may be elements besides the least element which have no predecessor (see below for an example). In a well-ordered set S, every subset T which has an upper bound has a least upper bound, namely the least element of the subset of all upper bounds of T in S. If ≤ is a non-strict well ordering, then < is a strict well ordering. A relation is a strict well ordering if and only if it is a well-founded strict total order.

The Japanese suffered heavy casualties in the battle around Oivi–Gorari, from 4 to 11 November. The well-ordered withdrawal that had been planned quickly disintegrated into a rout. The 7th Division was about from Buna–Gona. Although experience demanded caution, the way before them was clear of Japanese forces.

Heathcote School and Science College is a coeducational community secondary school and sixth form, located in the North Chingford area of the London Borough of Waltham Forest, England. Heathcote is a rapidly expanding, well- ordered and caring community committed to providing its young people with a rich and extensive education.

Like the related salt CeCl3, the bromide absorbs water on exposure to moist air. The compound melts congruently at 722 °C, and well ordered single crystals may be produced using standard crystal growth methods like Bridgman or Czochralski. CeBr3 adopts the hexagonal, UCl3-type crystal structure with P63/m Space group.

But he hasn't fashioned his tale from gossip. It is documented, with copious notes and attributions. The grace of these well-ordered snapshots is that there is no diatribe; you are left to put things together yourself. Human Smoke may be one of the most important books you will ever read.

Nevertheless, Kőnig continued his efforts to disprove parts of set theory. In 1905 he published a paper that claimed to prove that not all sets could be well-ordered. This statement was doubted by Cantor in a letter to Hilbert in 1906: Cantor was wrong. Today Kőnig's assumption is generally accepted.

Using the Von Neumann definition of ordinals, every ordinal is the well- ordered set of all smaller ordinals. The union of a nonempty set of ordinals that has no greatest element is then always a limit ordinal. Using Von Neumann cardinal assignment, every infinite cardinal number is also a limit ordinal.

Socoroma is a village in the Arica and Parinacota Region, Chile. It lies off Ruta 11 at km 99. It is an old Aymara settlement into which significant investment has been made to try to stop it from becoming a complete ghost town. It has a well-ordered church and plaza.

Australian forces maintained contact as the Japanese conducted a well-ordered rearguard action. The Allied objective was to eject the Japanese forces from these positions and deny them their further use. The Japanese forces were skillful, well prepared and resolute in their defence. They had developed a strong network of well- concealed defences.

There was ample evidence of this, such as his annulment of the 1628 Petition of Right, while he and Henrietta Maria openly told foreign ambassadors any concessions were temporary, and would be retrieved by force. It was also consistent with his approach in the Bishops' Wars, when he agreed peace terms with the Scots in 1639, before invading again in 1640. Regardless of religion or political belief, the vast majority in all three kingdoms were 'Royalist', in terms of believing a 'well-ordered' monarchy was divinely mandated. Where they disagreed was what 'well-ordered' meant, and who held ultimate authority, especially in clerical affairs; this mattered, because in the 17th century 'true religion' and 'good government' were assumed to be the same.

The Hausdorff maximal principle is an early statement similar to Zorn's lemma. Kazimierz Kuratowski proved in 1922 a version of the lemma close to its modern formulation (it applies to sets ordered by inclusion and closed under unions of well-ordered chains). Essentially the same formulation (weakened by using arbitrary chains, not just well-ordered) was independently given by Max Zorn in 1935, who proposed it as a new axiom of set theory replacing the well- ordering theorem, exhibited some of its applications in algebra, and promised to show its equivalence with the axiom of choice in another paper, which never appeared. The name "Zorn's lemma" appears to be due to John Tukey, who used it in his book Convergence and Uniformity in Topology in 1940.

These suspicions were enhanced after October 1641, when Irish Catholic rebels claimed his approval for their actions, an assertion given weight by previous attempts to use Irish troops against his Scottish opponents, and initial refusal to condemn the rebellion. However, Pym's understanding of Charles' character was hampered by the reality he was essential to a stable government and society. Regardless of religion or political belief, in 1642 the vast majority believed a 'well-ordered' monarchy was divinely mandated; where they disagreed was what 'well-ordered' meant, and who held ultimate authority in clerical affairs. Royalists generally supported a Church of England governed by bishops, appointed by, and answerable to, the king; Parliamentarians believed he was answerable to the leaders of the church, appointed by their congregations.

The class of von Neumann ordinals can be well- ordered. It cannot be a set (under pain of paradox); hence that class is a proper class, and all proper classes have the same size as V. Hence V too can be well-ordered. MK can be confused with second-order ZFC, ZFC with second- order logic (representing second-order objects in set rather than predicate language) as its background logic. The language of second-order ZFC is similar to that of MK (although a set and a class having the same extension can no longer be identified), and their syntactical resources for practical proof are almost identical (and are identical if MK includes the strong form of Limitation of Size).

Shadowing and blocking diffraction experiment to show the occurrence of premelting. The incident beam follows a crystal direction, so does the angle under which the detector is. The disorder of the quasi liquid premelt changes the scattering spectrum. There are several techniques to prove the existence of a liquid layer on a well-ordered surface.

Silicon is a fourfold coordinated atom that is normally tetrahedrally bonded to four neighboring silicon atoms. In crystalline silicon (c-Si) this tetrahedral structure continues over a large range, thus forming a well-ordered crystal lattice. In amorphous silicon this long range order is not present. Rather, the atoms form a continuous random network.

At that point a young magician by the name of Bodie, who had been watching the performance, tells then they should have used an old witch he knows, a Mrs. Jennings. They consult her in her small, well-ordered home. After a reading of tea-leaves, Mrs. Jennings announces that she knows what they need.

The eighth section contains eight maxims beginning with כל, but the initial and concluding maxims are not relevant to the proper matter of section. The ninth section is a well-ordered collection of twenty-eight maxims arranged in four paragraphs; seven of these maxims begin with אהוב, seven with הוי, and fourteen with אם.

His works often depict groups of figures, the principal subject always clearly located in the foreground. He uses bright colors, especially for clothing. In Knoller's work, individuals are dominant. He has a less rigid approach to classicism, the colours are less powerful while the composition is clear and well-ordered, free of Baroque pathos.

Every set formed at stage n can also be formed at every stage greater than n.Boolos (1998:88). Hence the stages form a nested and well-ordered sequence, and would form a hierarchy if set membership were transitive. The iterative conception has gradually become more accepted, despite an imperfect understanding of its historical origins.

On the other hand, the ordinals form an absolutely infinite sequence that cannot be increased in magnitude because there are no larger ordinals to add to it.Hallett 1986, pp. 41–42. In 1883, Cantor also introduced the well-ordering principle "every set can be well-ordered" and stated that it is a "law of thought".Moore 1982, p. 42.

Unlike Budd Hopkins and David Jacobs, folklorist Thomas Bullard could not identify a child presentation phase in the abduction narrative, even after undertaking a study of 300 abduction reports.Bullard, Thomas E. "The Well- Ordered Abduction: Pattern or Mirage?" In: Pritchard, Andrea & Pritchard, David E. & Mack, John E. & Kasey, Pam & Yapp, Claudia. Alien Discussions: Proceedings of the Abduction Study Conference.

His observatory has now been converted into the local polytechnic. Maharaja Narendra Shah was an enlightened ruler, as you can see in the well-ordered civic buildings of the neat little royal township of Narendranagar. Some of the buildings like the hospital and the secretariat are still in use today. The bazaar buildings too are a century old.

He wrote several books that had a substantial influence on Universalism in America in the twentieth century: The Social Implication of Universalism in 1915, A Religion for Greatness in 1945, and, posthumously, Worship and a Well Ordered Life published in 1959. The Unitarian Universalist Association's Skinner House Books imprint is named after him. Clarence Skinner died in 1949.

The axiom of choice is equivalent to the statement that every set can be well-ordered, i.e. that every cardinal has an initial ordinal. In this case, it is traditional to identify the cardinal number with its initial ordinal, and we say that the initial ordinal is a cardinal. The \alpha-th infinite initial ordinal is written \omega_\alpha.

This covers series, which is PM's term for what is now called a totally ordered set. In particular it covers complete series, continuous functions between series with the order topology (though of course they do not use this terminology), well- ordered series, and series without "gaps" (those with a member strictly between any two given members).

Dawes was present at the Battle of Shiloh, April 6–7, 1862, in southwestern Tennessee which was the most costly battle of the Civil War up to that point.White, 2016, p. 221 Dawes and the 53rd Ohio Infantry served with distinction, managing to keep well ordered during the otherwise chaotic battle. The 53rd was the vanguard of Sherman's line.

Each pair of distinct siblings is incomparable in . This is why the word unordered is used in the definition. Such a terminology might become misleading when all sibling sets are singletons, i.e. when the set of all nodes is totally ordered (and thus well-ordered) by In such a case we might speak about a singly-branching tree instead.

If a set is totally ordered, then the following are equivalent to each other: # The set is well ordered. That is, every nonempty subset has a least element. # Transfinite induction works for the entire ordered set. # Every strictly decreasing sequence of elements of the set must terminate after only finitely many steps (assuming the axiom of dependent choice).

In set theory, a tree is a partially ordered set (T, <) such that for each t ∈ T, the set {s ∈ T : s < t} is well-ordered by the relation <. Frequently trees are assumed to have only one root (i.e. minimal element), as the typical questions investigated in this field are easily reduced to questions about single-rooted trees.

In order theory, a different notion of a tree is used: an order-theoretic tree is a partially ordered set with one minimal element in which each element has a well-ordered set of predecessors. Every tree in descriptive set theory is also an order-theoretic tree, using a partial ordering in which two sequences T and U are ordered by T if and only if T is a proper prefix of U. The empty sequence is the unique minimal element, and each element has a finite and well-ordered set of predecessors (the set of all of its prefixes). An order-theoretic tree may be represented by an isomorphic tree of sequences if and only if each of its elements has finite height (that is, a finite set of predecessors).

In 1915, Hartogs could use neither von Neumann-ordinals nor the replacement axiom, and so his result is one of Zermelo set theory and looks rather different from the modern exposition above. Instead, he considered the set of isomorphism classes of well-ordered subsets of X and the relation in which the class of A precedes that of B if A is isomorphic with a proper initial segment of B. Hartogs showed this to be a well-ordering greater than any well-ordered subset of X. (This must have been historically the first genuine construction of an uncountable well-ordering.) However, the main purpose of his contribution was to show that trichotomy for cardinal numbers implies the (then 11 year old) well-ordering theorem (and, hence, the axiom of choice).

In December 2003, it emerged that 350 prisoners had absconded from Sudbury in five years. Management at the prison stated that this was a consequence of the prison having more inmates. In June 2005, an inspection report from Her Majesty's Chief Inspector of Prisons praised Sudbury Prison. The report stated that Sudbury provided a safe and well-ordered environment for prisoners and staff.

Georg Ferdinand Ludwig Philipp Cantor ( , ; – January 6, 1918Grattan-Guinness 2000, p. 351.) was a German mathematician. He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers.

William Ashford at Whyte's: Biographies or Irish Art and Irish Artists. Retrieved 22 March 2008. Ashford was among the most respected landscape painters of Ireland in his time, on par with Thomas Roberts and George Barret. Most of his works were topographical views of country seats and well-ordered parks and his principal patrons were, therefore, the nobility and landowners.

There are three usual operations on ordinals: addition, multiplication, and (ordinal) exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the operation or by using transfinite recursion. The Cantor normal form provides a standardized way of writing ordinals. It uniquely represents each ordinal as a finite sum of ordinal powers of ω.

Within a domain, however, the molecules are well ordered. LC materials may not always be in a liquid-crystal state of matter (just as water may turn into ice or water vapor). Liquid crystals can be divided into thermotropic, lyotropic and metallotropic phases. Thermotropic and lyotropic liquid crystals consist mostly of organic molecules, although a few minerals are also known.

Owner Kelly Hughes hosted a live in-store talk show called Kelly Hughes Live!, which has seen visits by writer Margaret Sweatman, comedian Kevin McDonald, children's entertainer Fred Penner and actor/politician Tina Keeper. The store was visited by journalist Noah Richler in 2009, who called it "one of the craziest, most amusing and well-ordered second-hand bookstores I have ever frequented".

Liquid organic electrolytes contain highly corrosive iodine, leading to problems of leakage, sealing, handling, dye desorption, and maintenance. Much attention is now focused on the electrolyte to address these problems. For solid-state dye sensitized solar cells, the first challenge originates from disordered titania mesoporous structures. Mesoporous titania structures should be fabricated with well-ordered titania structures of uniform size (~ 10 nm).

The further aim was to revive the glories of the old Tibetan Empire and create a peaceful and well-ordered Tsang.D. Templeman (2013), 'The 17th cent. gTsang rulers and their strategies of legitimation', p. 73 This was partly successful; the last remains of Rinpungpa authority vanished in 1590 as they were forced to capitulate their heartland Rong to Karma Tseten.

Each ordinal has an associated cardinal, its cardinality, obtained by simply forgetting the order. Any well-ordered set having that ordinal as its order type has the same cardinality. The smallest ordinal having a given cardinal as its cardinality is called the initial ordinal of that cardinal. Every finite ordinal (natural number) is initial, but most infinite ordinals are not initial.

The oldest is the Village, called "Byn" with the church from 1752, farms and old cultivated land. "Styrsö Tången" (Seaweed) is the traditional fishing village with dense buildings and winding narrow roads. In "Halsvik", the well-ordered seacaptains made their mark on the buildings and "Bratten" got the nice summer guests. Recent years Styrsö Sandvik has become a popular guest harbour for sailors.

In amorphous materials, the discussion of "dislocations" is inapplicable, since the entire material lacks long range order. These materials can still undergo plastic deformation. Since amorphous materials, like polymers, are not well-ordered, they contain a large amount of free volume, or wasted space. Pulling these materials in tension opens up these regions and can give materials a hazy appearance.

The magic angle artifact refers to the increased signal observed when MRI sequences with short echo time (TE) (e.g., T1 or proton density spin-echo sequences) are used to image tissues with well-ordered collagen fibers in one direction (e.g., tendon or articular hyaline cartilage). This artifact occurs when the angle such fibers make with the magnetic field is equal to θm.

Augustine of Hippo, City of God XI, ch. 4: "the world itself, by its well-ordered changes and movements, and by the fair appearance of all visible things, bears a testimony of its own, both that it has been created, and also that it could not have been created save by God, whose greatness and beauty are unutterable and invisible".

Depending on these specific chemical reactions, monomers are accurately added to the polymer chain and a well-ordered chain is accomplished stepwise. Meanwhile, by applying multiple chemical reactions, chemists have also developed multi- component reactions to accelerate the construction of polymer skeletons and also enhance variety. Beyond the aforementioned, there was a research group developing a molecule machine, which successfully achieve a sequence- controlled polymerization of oligopeptides.

Previously, soil and aquifers properties, mainly the permeability, were regarded as spatially homogeneous or well ordered. However, field measurements and even superficial observations, reveal that natural formations are generally heterogeneous. The spatial variability of permeability has a significant impact on water flow and contaminant spreading. Since medium properties vary in a seemingly erratic manner and measurements are generally scarce, their spatial distribution is subjected to uncertainty.

The least ordinal associated with a given cardinal is called the initial ordinal of that cardinal. Every finite ordinal (natural number) is initial, and no other ordinal associates with its cardinal. But most infinite ordinals are not initial, as many infinite ordinals associate with the same cardinal. The axiom of choice is equivalent to the statement that every set can be well-ordered, i.e.

FinSet is a full subcategory of Set, the category whose objects are all sets and whose morphisms are all functions. Like Set, FinSet is a large category. FinOrd is a full subcategory of FinSet as by the standard definition, suggested by John von Neumann, each ordinal is the well-ordered set of all smaller ordinals. Unlike Set and FinSet, FinOrd is a small category.

This stagnant absolutism ensured a stable, well-ordered society, but also resistance to social, cultural, or technological innovations. Reformers looked only to the past for inspiration. Literacy remained the province of the upper classes. Initially, Chinese was used for writing purposes, but by the 11th century, a set of derivative characters known as Chữ Nôm emerged that allowed native Vietnamese words to be written.

In 1992, the entire airfield was designated as a conservation area. English Heritage (now Historic England) later stated that "It embodies, to a unique degree, the improved architectural quality associated with the post-1934 expansion of the RAF. Most of the original buildings have survived and form a particularly coherent and well-ordered ensemble." Grade II listed buildings include the officers' mess and the church.

Mexico wanted to showcase its economic achievements and sought the international focus on the country. Maintaining an image of a prosperous and well-ordered Mexico was important for the Mexican government. However, things began to go badly wrong. In a relatively low-level conflict in late July 1968 between young people in Mexico City, the Granadero riot police used violence to tamp down the incident.

These children are labeled by experiencers as hybrids between humans and their abductors, usually Greys. Unlike Budd Hopkins and David Jacobs, folklorist Thomas E. Bullard could not identify a child presentation phase in the abduction narrative, even after undertaking a study of 300 abduction reports.Bullard, Thomas E. "The Well-Ordered Abduction: Pattern or Mirage?" In: Pritchard, Andrea & Pritchard, David E. & Mack, John E. & Kasey, Pam & Yapp, Claudia.

The village of old Puliakulam is very well ordered. The people belong to 12 different Kula Theivams having separate temple for each one of them, where the festivals are celebrated in the month of August (Tamil month of Aadi). There is also a temple for the primary deity of the village "Mariamman". The old martial arts of Wrestling and Silambam are still practiced and performed.

Other terms for this material are boronitrene or white graphene.Graphene and Boronitrene (White Graphene). physik.uni-saarland.de The boron nitride nanomesh is not only stable to decomposition under vacuum, air and some liquids, but also up to temperatures of 800 °C. In addition, it shows the extraordinary ability to trap molecules and metallic clusters which have similar sizes to the nanomesh pores, forming a well-ordered array.

Donald E. Strong, pp. 35–36 The ancient Greeks perceived order in the universe, and in turn, applied order and reason to their creations. Their humanist philosophy put mankind at the centre of things, and promoted well- ordered societies and the development of democracy. At the same time, the respect for human intellect demanded reason, and promoted a passion for enquiry, logic, challenge, and problem solving.

She also responds briefly to his tract in her second publication, Mortalities Memorandum. The second response came in 1617 from a writer under the pseudonym Esther Sowernam ("Sour"nam, as opposed to "Sweet"nam). Ester Hath Hang'd Haman is most notable for its reasoned and well-ordered argument. Next, also in 1617, was Worming of a Mad Dogge, by a writer under the pseudonym Constantia Munda.

Nixtun-Chʼichʼ is an Itza Maya archaeological site in Petén Department, Guatemala. It has an urban grid with fairly well ordered streets and avenues dated to around 2500 years ago. This is one of the earliest urban grids in the Americas and likely emerged as the ancient Maya developed more complex forms of political organization. It was likely a means to regulate and perhaps dominate the inhabitants.

The area has been long noted for its tree-lined, well-ordered streets, parks and a great variety of architecture, with century-old villas competing with late 20th-century modern housing. Following WWII increasing numbers of the larger properties were subdivided and smaller houses appeared. Since the early 1990s there has been a considerable amount of "infill" housing with clutches of townhouses altering the streetscapes in some parts of Epsom.

Basically it is all about showing that there is a phase on top of the solid which has hardly any order (quasi-liquid, see fig. order parameter). One possibility was done by Frenken and van der Veen using proton scattering on a lead (Pb) single crystal (110) surface. First the surface was atomically cleaned in [UHV], because one obviously has to have a very well ordered surface for such experiments.

On November 14, 2007, a cuneiform inscription dating back to Achaemenid era was discovered on Kharg Island in Old Persian. The inscription is carved on a coral rock in Old Persian semi-syllabic cuneiform signs. Despite the usually well-ordered regular system of Achaemenid inscriptions, this one is in an unusual order written in five lines. On May 31, 2008, the inscription was seriously damaged by unknown vandal(s).

300 burials was excavated during winter 2000–2001. The bones were analysed to determine the health and burial practices in the late medieval population of Northampton. 294 burials were uncovered in well ordered rows, with many wooden coffins, graves lined with old ceramic roof-tiles, stone-lined graves and a single stone coffin suggesting the occupants of relatively high status. Use of the cemetery later was less orderly.

To elucidate the structure of the cone walls, electron diffraction patterns were recorded at different cone orientations. Their analysis suggests that the walls contain 10–30% of ordered material covered with amorphous carbon. High-resolution electron microscopy reveals that the ordered phase consists of nearly parallel layers of graphene. The amorphous fraction can be converted into well-ordered graphite by annealing the cones at temperatures about 2700 °C.

Dong Zhongshu was a leading Confucian scholar in the Western Han dynasty, and was regarded as an authority on Gongyang Zhuan. Dong advocated According to Qing Dynasty scholar Kang Youwei's summary, some of Gongyang Zhuan's political agenda including the establishment of a well-ordered hierarchical regime (), a strong and centralized political authority (), and a merit-based civil government (), and a benevolent ruler whose legitimacy is based on the Mandate of Heaven.

Occurrence of gibbsite is always associated with these well-ordered kaolinites. Normally occurrence of hyper-aluminous clays due to the existence of gibbsite is one of the interesting subjects in the history of these kaolins. This causes many discussions about the origin of this mineral. The existence of gibbsite has been mentioned in the studies of Languine and Halm (1951), Caillere and Jourdain (1956), Kulbickie (1956), Dubreuilh et al.

On 4 July 1946, the Philippines became an independent nation. The fortifications of Jolo remained in good state during the American occupation when its walls, gates, and the buildings within it were photographed. Early 20th century photographs of Jolo show a well-ordered town, neatly laid out in a grid of streets and blocks—characteristics of Spanish urbanism applied with a military rigidity. In the postwar years the walls degraded.

Between such well-ordered societies, the principle of non-intervention should uphold. On the other hand, expansionist or human rights violating regimes are not shielded from the international law: in grave cases such as ethnic cleansing, coercive intervention by others is legitimate. Martha Nussbaum, however, is critical of Rawls' approach. She points out that the sufferings of individuals, not those of the impersonal states, form the moral foundations of humanitarian intervention.

It is inappropriate to distinguish between two well-ordered sets if they only differ in the "labeling of their elements", or more formally: if the elements of the first set can be paired off with the elements of the second set such that if one element is smaller than another in the first set, then the partner of the first element is smaller than the partner of the second element in the second set, and vice versa. Such a one-to-one correspondence is called an order isomorphism, and the two well-ordered sets are said to be order-isomorphic or similar (with the understanding that this is an equivalence relation). Formally, if a partial order ≤ is defined on the set S, and a partial order ≤' is defined on the set S' , then the posets (S,≤) and (S' ,≤') are order isomorphic if there is a bijection f that preserves the ordering. That is, f(a) ≤' f(b) if and only if a ≤ b.

In mathematics, specifically in axiomatic set theory, a Hartogs number is a particular kind of ordinal number. In particular, if X is any set, then the Hartogs number of X is the least ordinal α such that there is no injection from α into X. If X can be well-ordered then the cardinal number of α is a minimal cardinal greater than that of X. If X cannot be well-ordered then there cannot be an injection from X to α. However, the cardinal number of α is still a minimal cardinal not less than or equal to the cardinality of X. (If we restrict to cardinal numbers of well-orderable sets then that of α is the smallest that is not not less than or equal to that of X.) The map taking X to α is sometimes called Hartogs's function. This mapping is used to construct the aleph numbers, which are all the cardinal numbers of infinite well- orderable sets.

One of the methods of nanolithography is use of self- assembled monolayers (SAM) which develops soft methodology. SAMs are long chain alkanethiolates that are self-assembled on gold surfaces making a well- ordered monolayer films. The advantage of this method is to create a high quality structure with lateral dimensions of 5 nm to 500 nm. In this methodology a patterned elastomer made of polydimethylsiloxane (PDMS) as a mask is usually used.

The Regional Museum of Goeree-Overflakkee The Streekmuseum Goeree-Overflakkee (English: Regional Museum of Goeree-Overflakkee) is established in seven small houses dating back to the seventeenth century, in the old village of Sommelsdijk in the Netherlands. The buildings are inter-connected. The museum is subdivided into nineteen sections and there is an annually changing exhibition. All aspects of life and work on the island of Goeree-Overflakkee are shown in a well-ordered way.

Beemster is a municipality in the Netherlands, in the province of North Holland. The Beemster is the first so-called polder in the Netherlands that was reclaimed from a lake, the water being extracted from the lake by windmills. The Beemster Polder was dried during the period 1609 through 1612. It has preserved intact its well-ordered landscape of fields, roads, canals, dykes and settlements, laid out in accordance with classical and Renaissance planning principles.

For example, NBG implies that the proper class V can be well-ordered and that every proper class can be put into one-to-one correspondence with V. One consequence of conservative extension is that ZFC and NBG are equiconsistent. Proving this uses the principle of explosion: from a contradiction, everything is provable. Assume that either ZFC or NBG is inconsistent. Then the inconsistent theory implies the contradictory statements ∅ = ∅ and ∅ ≠ ∅, which are statements about sets.

Although well ordered nanostructures have already been successfully formed from self-assembling peptides, their potential will not be fully fulfilled until useful functionality is incorporated into the structures. Moreover, so far most of the peptide structures formed are in 1 or 2-D, whereas in nature most biological structures are in 3D.Shoseyov, O., I. Levy, and SpringerLink (Online service), NanoBioTechnology bioinspired devices and materials of the future. 2008, Humana Press: Totowa, N.J. p.

Confucius did not oppose capital punishment absolutely, but did take the view that in a well- ordered society based on moral persuasion, capital punishment would become unnecessary.Peimin Ni, Understanding the Analects of Confucius: A New Translation of Lunyu with Annotations (SUNY Press, 2017) pp. 293-94. During China's early dynasties, capital punishment and amputation were predominant among the five punishments. Later, amputation became less common, but capital punishment and corporal punishment remained.

Consequently, an isomorphism between two given well-ordered sets will be unique. #Cauchy's theorem on geometry of convex polytopes states that a convex polytope is uniquely determined by the geometry of its faces and combinatorial adjacency rules. #Alexandrov's uniqueness theorem states that a convex polyhedron in three dimensions is uniquely determined by the metric space of geodesics on its surface. #Rigidity results in K-theory show isomorphisms between various algebraic K-theory groups.

It is the true story of John Chapman, a college president who took a sabbatical and went out and got a job as a general laborer, to try to experience life outside his well-ordered but insulated college environment. The Secret Life of John Chapman was produced for CBS and generated a 44 share. Berlin Tunnel 21 was executive produced by Abrams in 1981. The film starred Richard Thomas, Horst Buchholz, and José Ferrer.

Among the urgent reforms then required in Poland were "a stable government, well ordered finances, and an army comparable with that of her neighbors." Oscar Halecki, A History of Poland (New York: Roy 1942; 9th ed., New York: David McKay 1976) at 191. The political system of the Rzeczpospolita was regarded by the nobility as the best in the world, and the Polish Sejm as (factuallyCronicae et gesta ducum sive principum Polonorum) the oldest.

The result is a partial order. If and are each totally ordered, then the result is a total order as well. The lexicographical order of two totally ordered sets is thus a linear extension of their product order. One can define similarly the lexicographic order on the Cartesian product of an infinite family of ordered sets, if the family is indexed by the nonnegative integers, or more generally by a well-ordered set.

There are various ways of well-ordering . Some of these involve the "fine structure" of , which was first described by Ronald Bjorn Jensen in his 1972 paper entitled "The fine structure of the constructible hierarchy". Instead of explaining the fine structure, we will give an outline of how could be well- ordered using only the definition given above. Suppose and are two different sets in and we wish to determine whether < or > .

Because the class of ordinal numbers is well-ordered, there is a smallest infinite limit ordinal; denoted by ω (omega). The ordinal ω is also the smallest infinite ordinal (disregarding limit), as it is the least upper bound of the natural numbers. Hence ω represents the order type of the natural numbers. The next limit ordinal above the first is ω + ω = ω·2, which generalizes to ω·n for any natural number n.

As distinguished from fantasy worlds or fictional universes aimed at the evocation of detailed worlds with well-ordered histories, geographies, and laws of nature, mythopoeia aims at imitating and including real-world mythology, specifically created to bring mythology to modern readers, and/or to add credibility and literary depth to fictional worlds in fantasy or science fiction books and movies. Mythopoeia are almost invariably created entirely by an individual, like the world of Middle-earth.

Different oils have different evaporation permeabilities, therefore yielding changes in concentration rates from different percipient/protein mixture. It is extremely difficult to predict good conditions for nucleation or growth of well-ordered crystals. In practice, favorable conditions are identified by screening; a very large batch of the molecules is prepared, and a wide variety of crystallization solutions are tested. Hundreds, even thousands, of solution conditions are generally tried before finding the successful one.

The red-tiled roof is divided into three main sections covering the nave and the extensions. At the western end of the building, it is crowned with an octagonal lantern and onion spire. The bright, yellow-tinted exterior with its onion spire is impressive enough. But those entering the double doors and proceeding through the small inner porch are struck by the rather sombre, well-ordered interior with its pious restraint and dominant altarpiece.

Some of the learning principles that good games incorporate include: identity development, interactive approaches, student production, risk-taking, individual customization, personal agency, well-ordered problems, challenges and consolidation, "just-in-time" and "on demand", situated meanings, systems thinking, active exploration, thinking laterally, rethinking goals, using smart tools and distributed knowledge, engaging in cross-functional teams, and encouraging performance before competence.Gee, James Paul. "Good video games and good learning." Phi Kappa Phi Forum, vol.

Ptolemy I died in January 282 aged 84 or 85. Shrewd and cautious, he had a compact and well-ordered realm to show at the end of forty years of war. His reputation for good nature and liberality attached the floating soldier-class of Macedonians and other Greeks to his service, and was not insignificant; nor did he wholly neglect conciliation of the natives. He was a ready patron of letters, founding the Great Library of Alexandria.

In short, she lives in a perfect world of success. But one day, it was called to her attention by her long-time accountant, Victor Carson that she is losing money without her knowledge from her financial records. Apparently, she is losing $25,000 monthly for the last three years. When Tallie finds out, she is completely at lost on how this has been happening since she fully trust that her well-ordered personal assistant, Brigitte takes care of everything.

Each microfibril is interdigitated with its neighboring microfibrils to a degree that might suggest they are individually unstable, although within collagen fibrils, they are so well ordered as to be crystalline. Three polypeptides coil to form tropocollagen. Many tropocollagens then bind together to form a fibril, and many of these then form a fibre. A distinctive feature of collagen is the regular arrangement of amino acids in each of the three chains of these collagen subunits.

The cofinality of an ordinal \alpha is the smallest ordinal \delta that is the order type of a cofinal subset of \alpha. Notice that a number of authors define cofinality or use it only for limit ordinals. The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set. Thus for a limit ordinal, there exists a \delta-indexed strictly increasing sequence with limit \alpha.

In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set which represents the operation or by using transfinite recursion. Cantor normal form provides a standardized way of writing ordinals. In addition to these usual ordinal operations, there are also the "natural" arithmetic of ordinals and the nimber operations.

There was no standard costume for slaves; they might dress well, badly, or barely at all, depending on circumstance and the will of their owner. Urban slaves in prosperous households might wear some form of livery; cultured slaves who served as household tutors might be indistinguishable from well-off freedmen. Slaves serving out in the mines might wear nothing. For Appian, a slave dressed as well as his master signalled the end of a stable, well-ordered society.

These can be found in pulse waves, square waves, boxcar functions, and rectangular functions. In digital signals the up and down transitions between high and low levels are called the rising edge and the falling edge. In digital systems the detection of these sides or action taken in response is termed edge-triggered, rising or falling depending on which side of rectangular pulse. A digital timing diagram is an example of a well-ordered collection of rectangular pulses.

Lignite formations are relatively frequent in Charentes clay deposits. Their thickness changes between some decimeters in lenses, to metric scale in continuous forms. These organic materials had some influences on kaolin deposited layers. Some of the observed influences are as follow: In gathered samples close to these organic materials, clays generally do not contain mica minerals, and especially in the neighborhood of Cuisian lignite, kaolinite is very well-ordered and the clay does not contain swelling clays with hydrazine.

This type of sand can have some influences on the leaching by mineral and organic acids produced by pyrite and organic materials, of the lower kaolin deposits. Thiry has found that generally these kaolins contain rather well- ordered kaolinite. Obviously, the level of crystallization can control technical properties of kaolinite as well as the structural impurities. The high energy current can interrupt the continuity of the settled layers of kaolin and reduce the simplicity of the estimation methods.

The electrified molten jet created via melt electrospinning has a more predictable path, and polymer fibers can be deposited accurately onto the collector. When the collector is moved at sufficient speed (referred to as the critical translation speed), straight melt electrospun fibers can be deposited in a layer upon layer approach. This enables for the fabrication of complex, well-ordered structures. In this respect melt electrospinning writing (MEW) can be considered a class of 3D printing.

Tranquillitas ordinis is a Latin phrase meaning the "tranquility of order" or "well-ordered concord". The term is associated with the Roman Catholic tradition of just war theory, and is found in the writings of Augustine of Hippo and Thomas Aquinas. Depending on the author and the context, the term is used to convey various meanings in theology and politics. These meanings include the divine order imposed on the universe and a theoretical framework for peace.

Mastrius had a well- ordered intellect which is seen in the clearness and precision with which he sets forth the subject-matter of discussion. His arguments for and against a proposition show real critical power and are expressed in accurate and clear language. His numerous quotations from ancient and contemporary authors and various schools of thought are a proof of his extensive reading. His works shed light on some of the difficult questions in Scotistic philosophy and theology.

The location, "Cary's Island" is fictitious, located north of Highway 17, past "Fisher's Falls" and near a village called "Brady". The house and estate, previously belonging to the Cary family, whose patriarch fought in the Napoleonic Wars, is called "Pennarth" (Welsh for "Bear's head"). Its octagonal layout was inspired by the writings of Orson Squire Fowler, which dates the building to the 1850s. The house is well-ordered and elaborate, and houses an extensive library of nineteenth century books.

Duke Henry II of the Babenberg dynasty elevated Vienna to his capital in 1155 In 976, the Margraviate of Ostarrîchi was given to the Babenberg family. Vienna lay at its border to Hungary. Vienna was an important site of trade as early as the 11th century. In the Exchange of Mautern between the Bishop of Passau and Margrave Leopold IV, Vienna is mentioned as a Civitas for the first time, which indicates the existence of a well-ordered settlement.

In 1905, the Hungarian mathematician Julius König published a paradox based on the fact that there are only countably many finite definitions. If we imagine the real numbers as a well- ordered set, those real numbers which can be finitely defined form a subset. Hence in this well-order there should be a first real number that is not finitely definable. This is paradoxical, because this real number has just been finitely defined by the last sentence.

Two students practicing kendo at Hiroshima University In the long feudal period governed by the samurai class, some methods that were used to train warriors were developed into well-ordered martial arts, in modern times referred to collectively as . Examples include , and sumo, all of which were established in the Edo period. After the rapid social change in the Meiji Restoration, some martial arts changed into modern sports, called . Judo was developed by , who studied some sects of jujutsu.

Somendra M. Bhattacharjee, and Avinash Khare, Fifty Years of the Exact Solution of the Two-Dimensional Ising Model by Onsager (1995), Now the dual of the discrete torus is itself. Moreover, the dual of a highly disordered system (high temperature) is a well-ordered system (low temperature). This is because the Fourier transform takes a high bandwidth signal (more standard deviation) to a low one (less standard deviation). So one has essentially the same theory with an inverse temperature.

In 1497 Rülein von Calw was appointed by the town of Freiberg as town physician (Stadtphysikus). Here he acted as a survey and construction engineer, mining expert and astrologer. In 1505 his book Eyn wohlgeordnet und nützlich büchlein, wie man bergwerk suchen und finden soll ("A well-ordered and useful little book about how to seek and find mines") appeared in Augsburg, the first scientific treatment of mining in Germany. As a doctor he fought the Plague in 1497.

Augustine of Hippo and Thomas Aquinas argue from the reference to "many mansions" that the mansions vary in type and therefore reflect "different degrees of rewards":Augustine, Homilies on the Gospel of John, Tractate 67, accessed 7 July 2016 :In every well-ordered city there is a distinction of mansions. Now the heavenly kingdom is compared to a city (). Therefore we should distinguish various mansions there according to the various degrees of beatitude.Thomas Aquinas, Summa Theologica, Question 93.

Though discovered in 1927, low energy electron diffraction did not become a popular tool for surface analysis until the early 1960s. The main reasons were that monitoring directions and intensities of diffracted beams was a difficult experimental process due to inadequate vacuum techniques and slow detection methods such as a Faraday cup. Also, since LEED is a surface sensitive method, it required well-ordered surface structures. Techniques for the preparation of clean metal surfaces first became available much later.

In its December 2016 Ofsted report the school was described as "inadequate" by Ofsted, with particular concerns about discipline, pupil progress, and finances. In January 2017, the head teacher Tom Sherrington abruptly left the school, which was put into special measures. This led to the school being taken over in September by the City of London Academy Trust. In September, Ofsted inspectors revisited the school and found a “well-ordered environment in which pupils behave well”.

Chapter 19 talks about how the acquisitions by Republics that are not well ordered and that do not proceed according to Roman virtue are for their ruin, not their exaltation. Chapter talks in detail about the different outlooks people have. Chapter 20 talks about and asks what danger the prince or republic runs that avails itself of Auxiliary or mercenary military. Says that having these services admits you are weak and is not something that is necessarily respectable.

Any approved minstrel taking on an apprentice and failing to provide the required years of training would be fined 40 shillings. All fines levied were divided between the stewards of the court and the Duchy of Lancaster (as John of Gaunt had held this title). The court looks to have created a well-ordered society of minstrels with pride in their work and as such to have functioned in a similar manner to the tradesmen's guilds of the period.

Such principles promote the common good and make for > a just and well-ordered society.Vermeule, Adrian (March 31, 2020) "Beyond > Originalism" The Atlantic Monthly Vermeule specified that common-good constitutionalism is "not tethered to particular written instruments of civil law or the will of the legislators who created them", so the stated purpose of the legislation is irrelevant to him. Yet he also says that "officials (including, but by no means limited to, judges)" will need "a candid willingness to 'legislate morality'" in order to create a "just and well-ordered society." The main aim of common-good constitutionalism: > is certainly not to maximize individual autonomy or to minimize the abuse of > power (an incoherent goal in any event), but instead to ensure that the > ruler has the power needed to rule well ... Just authority in rulers can be > exercised for the good of subjects, if necessary even against the subjects’ > own perceptions of what is best for them — perceptions that may change over > time anyway, as the law teaches, habituates, and re-forms them.

50 The success of reform contributed greatly to Russia's success in the Great Northern War; the increase in revenue and productivity increased the strength of the Russian war machine. More importantly, however, Peter created a "well-ordered police state"Cracraft, pg. 64 that further legitimized and strengthened authoritarian rule in Russia. A testament to this lasting influence are the many public institutions in the Soviet Union and the Russian Federation, such as Moscow State University, which trace their origins back to Peter's rule.

The most distinguishable feature of sequence-controlled polymers is the well- ordered chains composed of different repeating units. By encoding the repeating units, the correspondingly synthesized sequence-controlled polymer can be used for data storage. To modify the monomer with some bioactive moieties, the obtained sequence-controlled polymer is able to treat diseases. The property of sequence control make sequence-controlled polymers an ideal platform to install various kinds of pendants (like drugs, catalyst), whereby diverse functions and applications can be realized.

A convoy of merchant ships protected by airplanes en route to Cape Town during World War II A convoy is a group of vehicles, typically motor vehicles or ships, traveling together for mutual support and protection. Often, a convoy is organized with armed defensive support. It may also be used in a non- military sense, for example when driving through remote areas. Arriving at the scene of a major emergency with a well-ordered unit and intact command structure can be another motivation.

The build-up of enough ferrihydrite ions leads to nucleation, the rate of which can be altered via changing the pH at the site of nucleation. After one to two days, these ions are converted to goethite crystals.343x343pxThe unmineralized matrix consists of relatively well-ordered, densely packed arrays of chitin fibers, with only a few nanometers between adjacent fibers. The lack of space leads to the absence of pre-formed compartments within the matrix that control goethite crystal size and shape.

Since pore geometry affects the shape and curvature of an equilibrium meniscus, the Kelvin equation could be represented differently every time the meniscus changes along a "snake-like" capillary. This makes the analysis via the Kelvin equation complicated very quickly. Adsorption isotherm studies utilizing capillary condensation are still the main method for determining pore size and shape. With advancements in synthetic techniques and instrumentation, very well ordered porous structures are now available which circumvent the problem of odd-pore geometries in engineered systems.

Therefore, the concept of "well-ordered society," by falsely focusing on the state rather than individuals, cannot determine whether an intervention is justified. Instead, Nussbaum proposes a more concrete standard based on human capabilities (see Capability approach). She argues that "[n]ational sovereignty should be respected, within the constraints of promoting human capabilities". In other words, if a state fails to provide its citizens the basic "capabilities," such as the capability to live a healthy life, then outside intervention is justified.

In this section, juxtaposed variables such as indicate the product , and the standard order of operations is assumed. A total order on the natural numbers is defined by letting if and only if there exists another natural number where . This order is compatible with the arithmetical operations in the following sense: if , and are natural numbers and , then and . An important property of the natural numbers is that they are well-ordered: every non-empty set of natural numbers has a least element.

Decomposition of borazine on transition metal surfaces. Well-ordered nanomeshes are grown by thermal decomposition of borazine (HBNH)3, a colorless substance that is liquid at room temperature. The nanomesh results after exposing the atomically clean Rh(111) or Ru(0001) surface to borazine by chemical vapor deposition (CVD). The substrate is kept at a temperature of 796 °C (1070 K) when borazine is introduced in the vacuum chamber at a dose of about 40 L (1 Langmuir = 10−6 torr sec).

During this period, the German fleet reorganized into a well-ordered formation in reverse order, when the German light forces encountered the British screen shortly after 21:00. The renewed gunfire gained Beatty's attention, so he turned his battlecruisers westward. At 21:09, he sighted the German battlecruisers, and drew to within before opening fire at 20:20. In the ensuing melee, Seydlitz was hit several times; one shell struck the rear gun turret and other hit the ship's bridge.

The surface of Venus, as imaged by the Magellan probe using SAR A synthetic- aperture radar is an imaging radar mounted on a moving platform. Electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width.

Then there is a function G that maps F(A) onto V. Since the composite function G ∘ F maps A onto V, the axiom of limitation of size implies that A is a proper class, which contradicts A being a set. Therefore, F(A) is a set. Since the axiom of replacement implies the axiom of separation, the axiom of limitation of size implies the axiom of separation. Von Neumann also proved that his axiom implies that V can be well- ordered.

Ernst Zermelo (1904) gave a proof that every set could be well-ordered, a result Georg Cantor had been unable to obtain. To achieve the proof, Zermelo introduced the axiom of choice, which drew heated debate and research among mathematicians and the pioneers of set theory. The immediate criticism of the method led Zermelo to publish a second exposition of his result, directly addressing criticisms of his proof (Zermelo 1908a). This paper led to the general acceptance of the axiom of choice in the mathematics community.

In Williams youth, he went to join his uncle in the latter's evidently prosperous drapery story in Magherafelt, County Londonderry. A surviving photograph of the staff of the store is impressive: some fifty men and women in starched collars and prim blouses stand in well- ordered ranks. The move to Australia in 1913 followed the emigration of William's two brothers and a sister. His mother, formerly Helena Isabella Hutchinson, a schoolteacher, came from Knockboy, near Broughshane, County Antrim, of a family of schoolteachers and clerics.

Helen Gordon (1660-1687) was the wife of Thomas Gordon of Scotland, she died December 12, 1687, aged 27 years. Her tombstone is the oldest still erected in New Jersey. Her tombstone reads: "Calm was her death, well ordered her life, a pious mother and a loving wife, her offspring six, of which 4 here do lie, their souls in heaven, wher's do rest on high". In 1875 her tombstone and remains were moved from a cemetery on State Street to Saint Peter's Episcopal Church Cemetery.

Essentially, an ordinal is intended to be defined as an isomorphism class of well-ordered sets: that is, as an equivalence class for the equivalence relation of "being order-isomorphic". There is a technical difficulty involved, however, in the fact that the equivalence class is too large to be a set in the usual Zermelo–Fraenkel (ZF) formalization of set theory. But this is not a serious difficulty. The ordinal can be said to be the order type of any set in the class.

A classification system such as the SFI Group System will make a substantial contribution to standardized and well-ordered information related to ships/rigs, and will lead to improved communication both within a company and with external parties. The SFI Group System will make shipping and offshore operations more efficient because companies will save resources and avoid pitfalls when implementing the SFI standards. SFI can be the common denominator tying together all functions of shipping and offshore operations such as maintenance, purchasing, accounting, filing etc.

Gentzen's proof is the first example of what is called proof-theoretical ordinal analysis. In ordinal analysis one gauges the strength of theories by measuring how large the (constructive) ordinals are that can be proven to be well-ordered, or equivalently for how large a (constructive) ordinal can transfinite induction be proven. A constructive ordinal is the order type of a recursive well-ordering of natural numbers. Laurence Kirby and Jeff Paris proved in 1982 that Goodstein's theorem cannot be proven in Peano arithmetic.

There were also concerns that Allied forces might land at Buna at any time. The Allied advance across the Owen Stanley Range, 26 September – 15 November On 26 September, the Japanese began to withdraw. They fought a well-ordered rear-guard action back over the Owen Stanley Range, with the Australian 7th Division in close pursuit. The US 32nd Infantry Division had been sent to New Guinea in September and was ordered to make a circling move against the Japanese eastern flank near Wairopi.

Irregularity and local representativeness affect judgments of randomness. Things that do not appear to have any logical sequence are regarded as representative of randomness and thus more likely to occur. For example, THTHTH as a series of coin tosses would not be considered representative of randomly generated coin tosses as it is too well ordered. Local representativeness is an assumption wherein people rely on the law of small numbers, whereby small samples are perceived to represent their population to the same extent as large samples .

When the children were small their education was entrusted to their mother, Emilie. It was only when they were a little older that their father, who already had a busy work schedule, joined in the task. For the parents it was important that their children led a well ordered and properly scheduled day-to-day life. As soon as she was old enough, Amalie was required to submit, each evening, a work plan for the following day, with "Free hours" to be determined by her father.

One type of proof by contradiction is proof by descent, which proceeds first by assuming that something is possible, such as a positive integerMore generally, proof by infinite descent is applicable yo any well-ordered set. solution to a class of equations, and that therefore there must be a smallest solution. From the alleged smallest solution, it is then shown that a smaller solution can be found, contradicting the premise that the former solution was the smallest one possible—thereby showing that the original premise (that a solution exists) must be false.

Because if Christians are not well ordered from within, he says, if they do not put God first through a life of contemplation, they will be merely spreading their disorder to other people. "These world crises", he says, "are crises of saints." Thus, evangelization in Opus Dei is done one-on- one through its "apostolate of friendship and confidence." Peter L. Berger and Samuel Huntington calls the attempt of Opus Dei an "alternative modernity," a work towards a modern world which is "faithful" to the Christian traditions, as distinguished from other secular interventions in modernity.

Moscovici found that communication processes, the contents, and their consequences differed across the three social segments. Moscovici identified propaganda as the typical communication of the communist milieu, whereby communication is ordered systematically emphasising incompatibility and conflict. The intention is to generate negative stereotypes. Propagation was the typical form of the Catholic segment, identified as didactic and well-ordered but with the intention to make limited concessions to a subgroup of Catholics with affinities to psychoanalysis, and simultaneously, to set limits to the acceptance within the established orthodoxy of the Church.

"Tăslăuanu, p.249 As noted in 1913 by Luceafărul art columnist G. Duma, Sion took his painting "science" from French academies and "the grand masters", techniques from Synthetism in his religious work, and modern decorative elements in his landscapes.Duma, p.374 Duma describes Sion's 1913 paintings, especially Crai nou ("New Moon") and the Crucifixion, as a spiritual journey, and concludes: "In vibrant colors, with well-ordered planes, always directing us to the art of the future, the conscious painter Theodorescu-Sion dreams of and puts into song that aria which leads to immortality.

The cofinality of an ordinal α is the smallest ordinal δ which is the order type of a cofinal subset of α. The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set. Thus for a limit ordinal α, there exists a δ-indexed strictly increasing sequence with limit α. For example, the cofinality of ω² is ω, because the sequence ω·m (where m ranges over the natural numbers) tends to ω²; but, more generally, any countable limit ordinal has cofinality ω.

If an infinite set is a well-ordered set, then it must have a nonempty, nontrivial subset that has no greatest element. In ZF, a set is infinite if and only if the power set of its power set is a Dedekind-infinite set, having a proper subset equinumerous to itself.. See in particular pp. 32–33. If the axiom of choice is also true, then infinite sets are precisely the Dedekind-infinite sets. If an infinite set is a well-orderable set, then it has many well-orderings which are non-isomorphic.

Transfinite induction holds in any well-ordered set, but it is so important in relation to ordinals that it is worth restating here. : Any property that passes from the set of ordinals smaller than a given ordinal α to α itself, is true of all ordinals. That is, if P(α) is true whenever P(β) is true for all , then P(α) is true for all α. Or, more practically: in order to prove a property P for all ordinals α, one can assume that it is already known for all smaller .

The road climbs a hill southwards, out of Cromer, past Cromer Academy towards the next village of Northrepps and past the turning on the right of the A140 which is the main road to Norwich. Passing through well ordered arable farmland the road then reaches a cross roads, with the B1436 just before the village of Thorpe Market. The B1436 links the Cromer-Holt road to Mundesley on the coast. Out of the village the road runs along the boundary of Gunton Park, with some of deer park, on the right.

Although the Thaw marked a time of openness and liberalization primarily located in the public sphere, the emergence of private housing allowed for a new formulation of a private sphere in Soviet life.Susan E. Reid, "Cold War in the Kitchen: Gender and the De- Stalinization of Consumer Taste in the Soviet Union under Khrushchev," Slavic Review 61 (2002), 244. This resulted in a changing ideology that needed to make room for women, who were traditionally associated with the home, and consumption of goods in order to create a well-ordered "Soviet" home.

Stanley counted 125,000 troops marching off on a single campaign to the east, where a fleet of 230 war canoes waited to act as auxiliary naval support. In Buganda's capital, Stanley found a well-ordered town of about 40,000 surrounding the king's palace, which was situated atop a commanding hill. A wall more than four kilometers in circumference surrounded the palace compound, which was filled with grass- roofed houses, meeting halls, and storage buildings. At the entrance to the court burned the royal fire, which would only be extinguished when the kabaka died.

The school provides secondary education for pupils aged 11 – 16. Frederick Gent has a good and growing reputation as an innovative, high-achieving school with a well-ordered, caring and secure environment in which all youngsters can learn with confidence.OFSTED Report, March 2012 This was recognised by the school being designated as one of the first Leading Edge Schools. In the last few years the school has been transformed by moving into new buildings, becoming a Specialist Mathematics and ICT SchoolDFES Standards site accessed June 2007 in April 2004 and obtaining Artsmark Gold.

At the corners are the crow that symbolizes the Sun and the toad that symbolizes the Moon, the pairing of the Sun and Moon representing the cosmic forces of yin and yang.Ebrey (1999), 73; Hansen (2000), 121-123. The historian Sima Tan (d. 110 BCE) wrote that the Legalist tradition inherited by Han from the previous Qin dynasty taught that imposing severe man-made laws which were short of kindness would produce a well-ordered society, given that human nature was innately immoral and had to be checked.Csikszentmihalyi (2006), 24-25.

It was not until the 15th century that there developed single well-ordered religious communities with solemn vows and a common head. In the 15th century there were numerous independent male congregations of regular tertiaries with the three vows in Italy, Sicily, Dalmatia, Spain, Portugal, France, Germany, and in the Netherlands. The Obregonians, or the "Minim Congregation of Poor Brothers Infirmarians", were a small Spanish Roman Catholic congregation of men dedicated to the nursing care of the sick. The congregation ceased to exist around the time of the Peninsular War.

Sheffield Hallam University Public Art Archive: Details of Godfrey Sykes memorial. The park was opened to the public on Monday 6 September 1875 with the following day's Sheffield Daily Telegraph reporting: "The weather was fine. The Park looked in its gayest Summer dress. The walks were freshly gravelled, the flower beds were trim and well ordered." In 1882 the Weston Park Weather Station was erected privately by the curator of the adjacent museum; it is the official climatological station for Sheffield and since 1937 it has been run by the museum's staff.

Judgment of the Dead The paradigm of the city—the idea of the Good, the Agathon—has manifold historical embodiments, undertaken by those who have seen the Agathon, and are ordered via the vision. The centerpiece of the Republic, Part II, nos. 2–3, discusses the rule of the philosopher, and the vision of the Agathon with the allegory of the cave, which is clarified in the theory of forms. The centerpiece is preceded and followed by the discussion of the means that will secure a well-ordered polis (City).

In 1904 Ernst Zermelo proved by means of the axiom of choice (which was introduced for this reason) that every set can be well-ordered. In 1963 Paul J. Cohen showed that in Zermelo–Fraenkel set theory without the axiom of choice it is not possible to prove the existence of a well-ordering of the real numbers. However, the ability to well order any set allows certain constructions to be performed that have been called paradoxical. One example is the Banach–Tarski paradox, a theorem widely considered to be nonintuitive.

344 The Sassanian rulers always considered the advice of their ministers. A Muslim historian, Masudi, praised the "excellent administration of the Sasanian kings, their well-ordered policy, their care for their subjects, and the prosperity of their domains". In normal times, the monarchical office was hereditary, but might be transferred by the king to a younger son; in two instances the supreme power was held by queens. When no direct heir was available, the nobles and prelates chose a ruler, but their choice was restricted to members of the royal family.

The mound was found to be approximately deep and showed evidence of 11 periods of occupation spread over at least 1000 years between ca. 7400 and 6200 BC. The earliest levels, 11 to 8, showed early Neolithic aceramic occupation developing on to stages with pottery in levels 7 to 1, from which over 7000 sherds were recovered. Material from later levels was visible on the surface when first discovered. The layout and arrangement of houses seems to have been well ordered with similar arrangements of rooms, entrances, hearths and other features.

By the later stages of the Iron Age (1st century BC) and into the Roman Period (after 43 AD) a sizeable community had established itself at Ferry Lane Farm between Collingham and Besthorpe. Excavations by Manchester and Salford Universities took place for several summers until 2012. Though there is no suggestion of any significant material wealth, the site revealed a well-ordered system of rectilinear fields, closely spaced enclosures and trackways supporting theories of a relative increase in population densities. Similar sites have been recorded by aerial photography.

A construction of the surreal numbers as a maximal binary pseudo-tree with simplicity (ancestor) and ordering relations is due to Philip Ehrlich, The difference from the usual definition of a tree is that the set of ancestors of a vertex is well-ordered, but may not have a maximal element (immediate predecessor); in other words the order type of that set is a general ordinal number, not just a natural number. This construction fulfills Alling's axioms as well and can easily be mapped to the sign-sequence representation.

All real numbers which can be defined by a finite number of words form a subset of the real numbers. If the real numbers can be well-ordered, then there must be a first real number (according to this order) which cannot be defined by a finite number of words. But the first real number which cannot be defined by a finite number of words has just been defined by a finite number of words. (E) The smallest natural number without interesting properties acquires an interesting property by this very lack of any interesting properties.

In her epistle to the reader, Cavendish stated that with no children and, at that time, no estate, she had a lot of spare time. She, therefore, did not engage in housewifery, but filled her time with writing. She stated that good husbandry in poetry was well ordered fancy composed of fine language, proper phrases and significant words. Cavendish excused any errors that might be found in her work as due to her youth and inexperience, and explained that she wrote only to distract herself from thoughts of her husband's and her own hardships.

It is spectacularly visible how the molecules form a well-ordered array with the periodicity of the nanomesh (3.22 nm). The lower inset shows a region of this substrate with higher resolution, where individual molecules are trapped inside the pores. In addition, the molecules seem to keep their native conformation, what means that their functionality is kept, which is nowadays a challenge in nanoscience. Such systems with wide spacing between individual molecules/clusters and negligible intermolecular interactions might be interesting for applications such as molecular electronics and memory elements, in photochemistry or in optical devices.

Dragoons were intended to travel on horseback but fight on foot and were armed with carbines and pistols. Even orthodox cavalry carried firearms, especially the pistol, which they used in a tactic known as the caracole. Cavalry charges using swords on undisciplined infantry could still be quite decisive, but a frontal charge against well- ordered musketeers and pikemen was all but futile. Cavalry units, from the 16th century on, were more likely to charge other cavalry on the flanks of an infantry formation and try to work their way behind the enemy infantry.

It follows Kazu, a middle-age proprietress of an upscale Japanese restaurant that caters to politicians. She meets a semi- retired ambassador, Noguchi, grows to like him, and eventually marries him. From there the novel explores the conflicts that rise up between the two, as the tensions between the political world, Kazu's formerly well-ordered life, and Noguchi's integrity flare up. It is written in a distinctly Japanese style, betraying little of the interior emotions of the characters and dwelling on the minutiae of clothing and food in great detail.

Due to depth and precision of presentation of material, these books are defined as classical position in mathematical analysis. Book was translated, among others, into German, Chinese, and Persian however translation to English language has not been done still. Fichtenholz's books about analysis are widely used in Middle and Eastern European as well as Chinese universities due to its exceptionality of detailed and well-ordered presentation of material about mathematical analysis. Due to unknown reasons, these books do not have the same fame in universities in other areas of the world.

AllMusic reviewer Richard S. Ginell stated: "This record is the equivalent of throwing a stick of dynamite into a sedate, well-ordered dinner party, having the dynamite go off with a bang, and somehow leaving everything in its place. Such is the volatile Eric Dolphy, a serious wailer on the alto sax and even more idiosyncratic and radical on the bass clarinet, who barges into the lair of Juan Amalbert's Latin Jazz Quintet and doesn't perturb them in the least ... Not an ideal match, then, but fascinating without a doubt".

In A Theory of Justice, Rawls argues for a principled reconciliation of liberty and equality that is meant to apply to the basic structure of a well-ordered society. Central to this effort is an account of the circumstances of justice, inspired by David Hume, and a fair choice situation for parties facing such circumstances, similar to some of Immanuel Kant's views. Principles of justice are sought to guide the conduct of the parties. These parties are recognized to face moderate scarcity, and they are neither naturally altruistic nor purely egoistic.

He often gave judgments extempore and when reserved, litigants did not wait for long. His judgments were "well ordered, lucidly expressed in carefully chosen language and meticulous in their attention to the points in issue". He became an acting judge of appeal in 1957 and became a permanent member of the Appellate Division bench in June 1958. Thompson presided over the patent law case of Gentiruco v Firestone,Gentiruco v Firestone 1972 (1) SA 589 (A) which at the time was the longest appeal case heard by the Appellate Division.

The moral principles in the Scriptures ought to inform the civil magistrates, he believed, but he observed that well-ordered, just, and civil governments existed even where Christianity was not present. Thus, all governments had to maintain civil order and justice, but Williams decided that none had a warrant to promote or repress any religious views. Most of his contemporaries criticized his ideas as a prescription for chaos and anarchy, and the vast majority believed that each nation must have its national church and could require that dissenters conform.

This is different for a liquid film on the surface: This film does hardly (to the meaning of hardly see Landau theory) have any order. So the effects of shadowing and blocking vanish what means all the liquid film contributes the same amount of scattered electrons to the signal. Therefore, the peak does not only have a tail, but also becomes broadened. During their measurements Frenken and van der Veen raised the temperature to the melting point and hence could show that with increasing temperature a disordered film formed on the surface in equilibrium with a still well ordered Pb crystal.

In Zermelo–Fraenkel set theory without the axiom of choice (ZF), the following conditions are all equivalent: # S is a finite set. That is, S can be placed into a one-to-one correspondence with the set of those natural numbers less than some specific natural number. # (Kazimierz Kuratowski) S has all properties which can be proved by mathematical induction beginning with the empty set and adding one new element at a time. (See below for the set-theoretical formulation of Kuratowski finiteness.) # (Paul Stäckel) S can be given a total ordering which is well-ordered both forwards and backwards.

Cantor wanted the second paper to include a proof of the continuum hypothesis, but had to settle for expositing his theory of well-ordered sets and ordinal numbers. Cantor attempts to prove that if A and B are sets with A equivalent to a subset of B and B equivalent to a subset of A, then A and B are equivalent. Ernst Schröder had stated this theorem a bit earlier, but his proof, as well as Cantor's, was flawed. Felix Bernstein supplied a correct proof in his 1898 PhD thesis; hence the name Cantor–Bernstein–Schröder theorem.

More generally, the hyperbolic volume may be defined for any hyperbolic 3-manifold. The Weeks manifold has the smallest possible volume of any closed manifold (a manifold that, unlike link complements, has no cusps); its volume is approximately 0.9427.. Thurston and Jørgensen proved that the set of real numbers that are hyperbolic volumes of 3-manifolds is well-ordered, with order type .. The smallest limit point in this set of volumes is given by the knot complement of the figure-eight knot, and the smallest limit point of limit points is given by the complement of the Whitehead link.

Moreover, the hunger strike gained widespread sympathy from the population at large and earned the student movement the moral high ground that it sought. By the afternoon of 13 May, some 300,000 were gathered at the Square. Inspired by the course of events in Beijing, protests and strikes began at universities in other cities, with many students traveling to Beijing to join the demonstration. Generally, the demonstration at Tiananmen Square was well ordered, with daily marches of students from various Beijing-area colleges displaying their solidarity with the class boycott and with the demands of the protest.

He was on the editorial board of The American Historical Review and one correspondent with that journal quoted approvingly a Boyce review elsewhere where Boyce had said of the reviewed work: "For 364 pages of text there are almost 200 pages of notes. In the opinion of the writer these notes contain material that is not only essential for such a work, but include matter which is frequently as informing and exciting as the narrative itself. A remarkably rich and well-ordered bibliography of forty pages and indexes ... complete the book.""Communications", The American Historical Review, Vol.

White said soon after arriving in Boksburg that the place was one of the "most uninviting spots" he had ever seen. Two things dear to him were needed: a stream or well- ordered sheet of water and trees, instead of the barren area of muddy pools which he found. White was able to persuade a reluctant President to build a larger dam than was originally envisaged, because he visualised the ugly vlei being transformed into a beautiful lake fringed with trees. However, after completion, the new lake stood empty for nearly two years and became known as "White's folly".

Kelley, who had extensive experience with route surveying and knew the topography of the state extremely well, ordered the routes resurveyed again, a process which began in October 1847 and ended about the end of January 1848. Engineers Frederick Harbach and John Childe issued a new report to the board of directors on August 19, 1848. They confirmed that the two most-favored routes in 1846 were still the best, although several changes were identified which greatly improved them both. The engineers' preferred route (known as the Western Route), began in Cleveland and was long, with a ruling gradient of just 0.28 percent.

The protein's residues are mutated one by one to identify residue clusters that are well-ordered in the folded transition state. These residues' interactions can be checked by double-mutant-cycle \phi analysis, in which the single-site mutants' effects are compared to the double mutants'. Most mutations are conservative and replace the original residue with a smaller one (cavity-creating mutations) like alanine, though tyrosine-to-phenylalanine, isoleucine-to-valine and threonine-to-serine mutants can be used too. Chymotrypsin inhibitor, SH3 domains, individual domains of proteins L and G, ubiquitin, and barnase have all been studied by \phi analysis.

The fact that the Kleene–Brouwer order is a linear ordering (that is, that it is transitive as well as being total) follows immediately from this, as any three sequences on which transitivity is to be tested form (with their prefixes) a finite tree on which the Kleene–Brouwer order coincides with the postorder. The significance of the Kleene–Brouwer ordering comes from the fact that if X is well-ordered, then a tree over X is well-founded (having no infinitely long branches) if and only if the Kleene–Brouwer ordering is a well-ordering of the elements of the tree.

The original meaning of shen "god; spirit; deity" was also a religious concept. External spirits were believed to occasionally descend to human beings (particularly shamans), or humans could draw them down with the power of de "inner power; virtue" (Harper 1998: 119). Verse 13 describes the aspects of shen "numen; numinous": > There is a numinous [mind] naturally residing within [有神自在身]; One moment it > goes, the next it comes, And no one is able to conceive of it. If you lose > it you are inevitably disordered; If you attain it you are inevitably well > ordered.

Charles Lodge (William Powell), a free-spirited bohemian who lives in a cluttered car trailer, disrupts the well-ordered life of successful, hardworking businesswoman Margit Agnew (Myrna Loy) when he convinces her younger sister Irene (Florence Rice) that she should become an actress. However, Margit is determined that Irene marry the fiancé she (and her mother before) had personally picked out for her sister, the pliable, weak-willed cousin Waldo (John Beal). Fed up with Waldo's lack of initiative during a four-year engagement, Irene becomes infatuated with Charles. He pretends to return her feelings so he can stay close to Margit.

The IMRAD structure has proved successful because it facilitates literature review, allowing readers to navigate articles more quickly to locate material relevant to their purpose. But the neat order of IMRAD rarely corresponds to the actual sequence of events or ideas of the research presented; the IMRAD structure effectively supports a reordering that eliminates unnecessary detail, and allows the reader to assess a well-ordered and noise-free presentation of the relevant and significant information. It allows the most relevant information to be presented clearly and logically to the readership, by summarizing the research process in an ideal sequence and without unnecessary detail.

They associated on equal terms with laymen of the highest distinction, and shared all their pleasures and pursuits. This rank and power was, however, often used most beneficially. For instance, we read of Richard Whiting, the last abbot of Glastonbury, judicially murdered by Henry VIII, that his house was a kind of well-ordered court, where as many as 300 sons of noblemen and gentlemen, who had been sent to him for virtuous education, had been brought up, besides others of a lesser rank, whom he fitted for the universities. His table, attendance and officers were an honour to the nation.

In addition to these exceptional stabilities, the nanomesh shows the extraordinary ability to act as a scaffold for metallic nanoclusters and to trap molecules forming a well-ordered array. In the case of gold (Au), its evaporation on the nanomesh leads to formation of well-defined round Au nanoparticles, which are centered at the nanomesh pores. The STM figure on the right shows Naphthalocyanine (Nc) molecules, which were vapor-deposited onto the nanomesh. These planar molecules have a diameter of about 2 nm, whose size is comparable to that of the nanomesh pores (see upper inset).

If the graph is countable, the vertices are well-ordered and one can canonically choose the smallest suitable vertex. In this case, Kőnig's lemma is provable in second-order arithmetic with arithmetical comprehension, and, a fortiori, in ZF set theory (without choice). Kőnig's lemma is essentially the restriction of the axiom of dependent choice to entire relations R such that for each x there are only finitely many z such that xRz. Although the axiom of choice is, in general, stronger than the principle of dependent choice, this restriction of dependent choice is equivalent to a restriction of the axiom of choice.

Farnese, seeing that his attack was going well, ordered Olivera to advance with his cavalry to support the infantry's push. While the light horsemen penetrated into Borgerhout across the breach opened by Figueroa's men, Farnese himself took the command of Taxis' lancers and did the same across Valdés' path. The French and English soldiers offered a strong resistance, but after two hours of battle inside the quarters, De la Noue began to withdraw his forces to Antwerp to avoid destruction. The retreating troops set fire to their lodgements and looked for shelter under the coverage of Antwerp's artillery.

The standard ordering ≤ of the natural numbers is a well ordering and has the additional property that every non-zero natural number has a unique predecessor. Another well ordering of the natural numbers is given by defining that all even numbers are less than all odd numbers, and the usual ordering applies within the evens and the odds: :0 2 4 6 8 ... 1 3 5 7 9 ... This is a well-ordered set of order type ω + ω. Every element has a successor (there is no largest element). Two elements lack a predecessor: 0 and 1.

There was no cavalry in western Europe capable of consistently breaking a well-ordered shieldwall, aside perhaps from the Byzantine Cataphracts. This was due to the relatively small size of horses, and the fact that, even with the advent of the couched lance in the 12th century, well disciplined spearmen still presented a major problem for cavalry. This was demonstrated at Hastings when the Normans, who probably were the best cavalry of the period, tried all day to break the Anglo-Saxon line. To judge the effectiveness of any military formation one first needs to determine what was its function.

A very well known example of surface reconstruction occurs in silicon, a semiconductor commonly used in a variety of computing and microelectronics applications. With a diamond-like face-centered cubic (fcc) lattice, it exhibits several different well-ordered reconstructions depending on temperature and on which crystal face is exposed. When Si is cleaved along the (100) surface, the ideal diamond-like structure is interrupted and results in a 1×1 square array of surface Si atoms. Each of these has two dangling bonds remaining from the diamond structure, creating a surface that can obviously be reconstructed into a lower-energy structure.

The place has aesthetic value for its sense of dramatic isolation and ruin within the surrounding well-ordered oil refinery, and for the panoramic views both from and to the hill. The place has a strong or special association with a particular community or cultural group for social, cultural or spiritual reasons. The site is significant socially for its association with the development of military culture in Queensland from the 1880s to the 1930s; and as the site of the Reformatory where boys were educated and trained in Queensland in the last two decades of the 19th century.

Ostensibly, she confiscates Jemima's eggs believing Jemima will abandon them, but the eggs are not confiscated for the well-being of Jemima and her kin but for the well-being of the farmer's wife and her family: the eggs (or the ducks hatched from them) will end up on their dinner table. In this respect, the farmer's wife is a predator like the fox, but the fox is condemned for his predation. Human values are at the top of the tale's hierarchy. Potter argues for the well- ordered home and the practicalities of farm life over the fantasy lives of animals.

In Addition, in order to assist the economy in preparation for cyber threats, the NCSA published in early 2017 the "Organizational Cyber Defence Methodology". It supplies every organization in Israel, be it large or small, with tools for the management and optimization of its defense against the risks of cyber threats, and assists it with devising a well-ordered work plan. Thousands of Israeli organizations are already working according to this methodology, which is accessible to all as a free service rendered to the Israeli economy (pdf). Meanwhile, the NCSA has invested efforts in promoting a professional cyber nationwide work force.

Bernhard Karlgren called his style straightforward and without literary pretensions; in general, modern Western writers have noted that Wang was one of the most original thinkers of his time, even iconoclastic in his opinions. They note that he gained popularity in the early 20th century because his ideas correspond to those that later evolved in Europe. His writing is praised for being clear and well ordered. But, because there was no functioning scientific method or larger scientific discourse in his time, his formulations can seem alien to the modern eye — to some readers, even as peculiar as the superstitions that he was rejecting.

The principle of complete induction is not only valid for statements about natural numbers but for statements about elements of any well-founded set, that is, a set with an irreflexive relation < that contains no infinite descending chains. Any set of cardinal numbers is well-founded, which includes the set of natural numbers. Applied to a well-founded set, it can be formulated as a single step: # Show that if some statement holds for all , then the same statement also holds for n. This form of induction, when applied to a set of ordinals (which form a well-ordered and hence well-founded class), is called transfinite induction.

However, powerful patrons, including the local bishop, coupled with the impression of well ordered subsistence and purpose, turned animosity into approval. In March 1563, after Teresa had moved to the new convent house, she received papal sanction for her primary principles of absolute poverty and renunciation of ownership of property, which she proceeded to formulate into a "constitution". Her plan was the revival of the earlier, stricter monastic rules, supplemented by new regulations including the three disciplines of ceremonial flagellation prescribed for the Divine Office every week, and the discalceation of the religious. For the first five years, Teresa remained in seclusion, mostly engaged in prayer and writing.

He was not drinking after his departure from Moscow and was enthusiastic about leaving the capital and working on other new texts. A project he was dreaming about was close to success: to start editing a literature magazine of his own. Most of his manuscripts were missing from his hotel room and had never been discovered (including his recently announced novella known under the work title When I was a boy… and his winter poems from the last months). Yesenin preferred to be well ordered in his work; but his hotel room was in extreme chaos, with his things scattered on the floor and with signs of a fight.

Boarding actions and hand-to-hand fighting determined the outcome of most naval battles in the Middle Ages. Here the Byzantine dromons are shown rolling over the Rus' vessels and smashing their oars with their spurs. On the approach to and during an actual battle, a well-ordered formation was critical: if a fleet fell into disorder, its ships would be unable to lend support to each other and probably would be defeated. Fleets that failed to keep an ordered formation or that could not order themselves into an appropriate counter-formation (antiparataxis) to match that of the enemy, often avoided, or broke off from battle.

Oliver Brownson (born 13 May 1746 in Bolton, Connecticut — died 20 Oct 1815 in Smithfield, New York) was an American composer and music editor, who lived in Connecticut for much of his life. In 1775 he married Sarah Merrels, and they had at least one child. Oliver Brownson was a singing master in Connecticut during the last quarter of the 18th Century.Grove Music Online: Brownson, Oliver (1746 - 1815), composer, singing master, printer Among his most well- known tunes are: Colchester ("Great God, the heav'ns well-ordered frame"); Norfolk ("Alas, the brittle clay"); Salisbury ("God of my salvation, hear"); and Virginia ("Thy words the raging wind control").

Her reading was extensive and varied, her memory retentive, her adaptation rapid, and her language forcible and graceful. She was the centre of a large circle, which numbered among its members many of the brightest names in literature. The head of a well ordered household, a tender and devoted wife and mother, an active and sympathizing friend, she passed many years in a constant discharge of her varied duties. Beginning in the late 1840s, she was stricken down by an illness from which she never rallied, and for the last few years of her life, she became an invalid, totally withdrawn from the world.

Things then improved somewhat, and Vale Royal's last years were peaceful and well-ordered. Some building work continued, as records attest to grants of timber for repairs were made in 1510 and 1515. The abbot of Dore visited Vale Royal in 1509—by which time the abbey held 19 monks—and made a brief inventory of its rooms, including the Abbot's chambers (which were described as containing "a suitable couch, ten coverlets, four mattresses, two feather beds and twelve pairs of linen sheets"). According to archaeologist S. J. Moorhouse, luxuries such as these indicate how far the Cistercian focus had drifted from the order's original asceticism.

If the form of the contradiction is that we can derive a further counterexample D, that is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called proof by infinite descent. In which case, there may be multiple and more complex ways to structure the argument of the proof. The assumption that if there is a counterexample, there is a minimal counterexample, is based on a well-ordering of some kind. The usual ordering on the natural numbers is clearly possible, by the most usual formulation of mathematical induction; but the scope of the method can include well-ordered induction of any kind.

We obtain the finite rooted tree representing α by joining the roots of the trees representing \beta_1,\ldots,\beta_k to a new root. (This has the consequence that the number 0 is represented by a single root while the number 1=\omega^0 is represented by a tree containing a root and a single leaf.) An order on the set of finite rooted trees is defined recursively: we first order the subtrees joined to the root in decreasing order, and then use lexicographic order on these ordered sequences of subtrees. In this way the set of all finite rooted trees becomes a well-ordered set which is order- isomorphic to ε0.

It was a period in which the State and the government itself led the city's cultural life and progress, promoting and funding new activities and rewarding the most deserving citizens and achievements.Mazzocca, 46 During this initial period, Neoclassicism was characterized by a more sober and austere approach, resulting in symmetrical, well-ordered structures. The Napoleonic period, while demonstrating some continuity in reinitiating work suspended under the Austrian government, was also characterized by a more monumental and celebratory style, striving to promote Milan as one of the great European capitals with Eclectic and Romantic architectural features. In particular, outstanding new roads and city gates were completed.

Pore-lining carbonyl groups are well situated to stabilize hydronium ions via second-shell interactions involving bridging water molecules. A collective switch of hydrogen bond orientations may contribute to the directionality of proton flux as His37 is dynamically protonated and deprotonated in the conduction cycle. The His37 residues form a box-like structure, bounded on either side by water clusters with well-ordered oxygen atoms near by. The conformation of the protein, which is intermediate between structures previously solved at higher and lower pH, suggests a mechanism by which conformational changes might facilitate asymmetric diffusion through the channel in the presence of a proton gradient.

In the late 1920s Le Corbusier lost confidence in big business to realise his dreams of utopia represented in the Ville Contemporaine and Plan Voisin (1925). Influenced by the linear city ideas of Arturo Soria y Mata (which Milyutin also employed) and the theories of the syndicalist movement (that he had recently joined) he formulated a new vision of the ideal city, the Ville Radieuse. It represented a utopian dream to reunite man within a well-ordered environment. Unlike the radial design of the Ville Contemporaine, the Ville Radieuse was a linear city based upon the abstract shape of the human body with head, spine, arms and legs.

However, this existence theorem is purely theoretical, as such a base has never been explicitly described. The well-ordering theorem implies that the real numbers can be well-ordered if the axiom of choice is assumed: there exists a total order on R with the property that every non-empty subset of R has a least element in this ordering. (The standard ordering ≤ of the real numbers is not a well-ordering since e.g. an open interval does not contain a least element in this ordering.) Again, the existence of such a well-ordering is purely theoretical, as it has not been explicitly described.

Initially, the droplet of protein solution contains comparatively low precipitant and protein concentrations, but as the drop and reservoir equilibrate, the precipitant and protein concentrations increase in the drop. If the appropriate crystallization solutions are used for a given protein, crystal growth occurs in the drop.Rhodes, G. (2006) Crystallography Made Crystal Clear, Third Edition: A Guide for Users of Macromolecular Models, 3rd Ed., Academic Press This method is used because it allows for gentle and gradual changes in concentration of protein and precipitant concentration, which aid in the growth of large and well-ordered crystals. Vapor diffusion can be performed in either hanging-drop or sitting-drop format.

Magnetotactic bacteria are widespread, motile, diverse prokaryotes that biomineralize a unique organelle called the magnetosome. A magnetosome consists of a nano-sized crystal of a magnetic iron mineral, which is enveloped by a lipid bilayer membrane. In the cells of most all magnetotactic bacteria, magnetosomes are organized as well-ordered chains. The magnetosome chain causes the cell to behave as a motile, miniature compass needle where the cell aligns and swims parallel to magnetic field lines. The magnetic dipole moment of the cell is often large enough that its interaction with Earth’s magnetic field overcomes the thermal forces that tend to randomize the orientation of the cell in its aqueous surroundings.

This is all the more true when we consider just what this might mean for a well-ordered free and democratic society. However, extreme care should be taken not to assume Scheler’s philosophy is somehow based purely in some sort of progressive bottom-up psychology: for example, Abraham Maslow’s hierarchy of needs, Jean Piaget’s theory of cognitive development, or Lawrence Kohlberg’s Stages of Moral Development. This is particularly important since Scheler’s relied extensively on hierarchical “stratification” models as a sort of general motifHierarchy of Model Person Types from lowest to highest: the Bon Vivant, the Hero, the Genius and the Saint. (See Formalism, p. 585).

In 1910 Perkins began to pursue Progressive Era reform causes. Perkins was an articulate exponent of the evils of competition and the advantages of cooperation in business-- he believed in the Good Trust. His biographer, John A. Garraty, summarized Perkins' business philosophy as follows: :"The fundamental principle of life is co-operation rather than competition... Competition is cruel, wasteful, destructive, outmoded; co-operation, inherent in any theory of a well-ordered Universe, is humane, efficient, inevitable and modern." John A. Garraty, Right-hand Man: the life of George W. Perkins (1978) p 216 In 1912 he helped organize Theodore Roosevelt's new Progressive party, becoming its executive secretary.

It involved control over nature, hierarchical bureaucracy, rules and regulations, control and categorisation — all of which attempted to remove gradually personal insecurities, making the chaotic aspects of human life appear well-ordered and familiar. Bauman in 2011 Later in a number of books Bauman began to develop the position that such order-making never manages to achieve the desired results. When life becomes organised into familiar and manageable categories, he argued, there are always social groups who cannot be administered, who cannot be separated out and controlled. In his book Modernity and Ambivalence Bauman began to theorise about such indeterminate persons in terms of an allegorical figure he called, 'the stranger.

Many authors use other terms in place of "Euclidean function", such as "degree function", "valuation function", "gauge function" or "norm function". Some authors also require the domain of the Euclidean function to be the entire ring ; however this does not essentially affect the definition, since (EF1) does not involve the value of . The definition is sometimes generalized by allowing the Euclidean function to take its values in any well- ordered set; this weakening does not affect the most important implications of the Euclidean property. The property (EF1) can be restated as follows: for any principal ideal of with nonzero generator , all nonzero classes of the quotient ring have a representative with .

In December 1638, bishops were expelled from the kirk; when Charles attempted to use military force, he was defeated in the 1639 and 1640 Bishops' Wars, which left the Covenanter party in control of Scotland. Calvinists believed a 'well-ordered' monarchy was part of God's plan; as a result, the vast majority of Covenanters agreed monarchy itself was divinely ordered but disagreed on who held ultimate authority in clerical affairs. Royalists and Engagers tended to argue the king held supreme authority, but that did not necessarily mean they supported bishops and individual motives were very complex. Many fought for both Covenant and king at different times, including Montrose.

A chunk of armor blown off Moltke during the Battle of Jutland A pause in the battle at dusk allowed Moltke and the other German battlecruisers to cut away wreckage that interfered with the main guns, extinguish fires, repair the fire control and signal equipment, and ready the searchlights for nighttime action. During this period, the German fleet reorganized into a well-ordered formation in reverse order, when the German light forces encountered the British screen shortly after 21:00. The renewed gunfire gained Beatty's attention, so he turned his battlecruisers westward. At 21:09, he sighted the German battlecruisers, and drew to within before opening fire at 20:20.

Counting in the everyday sense typically starts from one, so it assigns to each object the size of the initial segment with that object as last element. Note that these numbers are one more than the formal ordinal numbers according to the isomorphic order, because these are equal to the number of earlier objects (which corresponds to counting from zero). Thus for finite n, the expression "n-th element" of a well-ordered set requires context to know whether this counts from zero or one. In a notation "β-th element" where β can also be an infinite ordinal, it will typically count from zero.

In the choice of a classical style of architecture, central location and arrangement of spaces - a spacious banking chamber combined with shops, tenantable offices and residential accommodation on the roof level - the Westpac Bank is important in illustrating the principal characteristics of an interwar bank in a regional centre. The place is important because of its aesthetic significance. A fine example of the commercial architecture of Francis Richard Hall, the Westpac Bank, with its well-ordered and classically proportioned facades, contributes to the Flinders Street streetscape. The place has a special association with the life or work of a particular person, group or organisation of importance in Queensland's history.

His 1972 book How To Do Things Right: The Revelations of a Fussy Man was a set of humorous essays filled with obsessively-detailed instructions on, for example, the correct way to make and eat milk-toast and clean ashtrays which "throughout its whole lifetime in a well-ordered household,an ashtray need never travel more than three feet from where it belongs, and never be out of place at all for more than thirty seconds". In 1974 he edited "Writer's Choice" a collection of short stories. The writers included picked their personal favorite of their own work. Contributors included Updike, Mailer, Capote, Southern, Barth and Roth.

More generally, it is a theorem of ZF that any well-ordered set can be enumerated under this characterization so that it coincides up to relabeling with the generalized listing enumeration. If one also assumes the Axiom of Choice, then all sets can be enumerated so that it coincides up to relabeling with the most general form of enumerations. Since set theorists work with infinite sets of arbitrarily large cardinalities, the default definition among this group of mathematicians of an enumeration of a set tends to be any arbitrary α-sequence exactly listing all of its elements. Indeed, in Jech's book, which is a common reference for set theorists, an enumeration is defined to be exactly this.

Conversely, any set S of ordinals that is downward-closed -- meaning that for any ordinal α in S and any ordinal β < α, β is also in S -- is (or can be identified with) an ordinal. There are infinite ordinals as well: the smallest infinite ordinal is \omega, which is the order type of the natural numbers (finite ordinals) and that can even be identified with the set of natural numbers. Indeed, the set of natural numbers is well-ordered—as is any set of ordinals—and since it is downward closed, it can be identified with the ordinal associated with it (which is exactly how \omega is defined). A graphical "matchstick" representation of the ordinal ω².

The original definition of ordinal numbers, found for example in the Principia Mathematica, defines the order type of a well-ordering as the set of all well-orderings similar (order-isomorphic) to that well-ordering: in other words, an ordinal number is genuinely an equivalence class of well-ordered sets. This definition must be abandoned in ZF and related systems of axiomatic set theory because these equivalence classes are too large to form a set. However, this definition still can be used in type theory and in Quine's axiomatic set theory New Foundations and related systems (where it affords a rather surprising alternative solution to the Burali-Forti paradox of the largest ordinal).

Scott's trick assigns representatives differently, using the fact that for every set A there is a least rank γA in the cumulative hierarchy when some set of the same cardinality as A appears. Thus one may define the representative of the cardinal number of A to be the set of all sets of rank γA that have the same cardinality as A. This definition assigns a representative to every cardinal number even when not every set can be well-ordered (an assumption equivalent to the axiom of choice). It can be carried out in Zermelo-Fraenkel set theory, without using the axiom of choice, but making essential use of the axiom of regularity.

Khwaday-Namag: Ibn al-Muqaffa' is thought to have produced an Arabic adaptation of the late Sasanian Khwaday-Namag, a chronicle of pre-Islamic Persian kings, princes, and warriors. A mixture of legend, myth, and fact, it served as a quasi-national history inspired by a vision of kingship as a well-ordered autocracy with a sacred duty to rule and to regulate its subjects’ conduct within a rigid class system. Interspersed with maxims characteristic of andarz literature, the narrative also offered practical advice on civil and military matters. Ibn al- Muqaffa' is known to have modified certain parts of the original and excluded others, possibly to make it intelligible to his Arab Muslim readers.

They were: the Arcadian (from Arcadia), Achaean (from Achaea), Elean (from Elea), Boeotian (from Boeotia), Amphictyonic (from Amphictyonis), Dorian (from Doris), Ionian (from Ionia), Athenian (from Athens), Euboean (from Euboea), and Nesiotic (from the islands).Diod. xii. 11. The form of government was democratic, and the city is said to have enjoyed the advantage of a well-ordered system of laws; but the statement of Diodorus, who represents this as owing to the legislation of Charondas, and that lawgiver himself as a citizen of Thurii, is certainly erroneous. The city itself was laid out with great regularity, being divided by four broad streets or plateae, each of which was crossed in like manner by three others.Diod. xii. 10.

In descriptive set theory, the Kleene–Brouwer order or Lusin–Sierpiński order is a linear order on finite sequences over some linearly ordered set (X, <), that differs from the more commonly used lexicographic order in how it handles the case when one sequence is a prefix of the other. In the Kleene–Brouwer order, the prefix is later than the longer sequence containing it, rather than earlier. The Kleene–Brouwer order generalizes the notion of a postorder traversal from finite trees to trees that are not necessarily finite. For trees over a well-ordered set, the Kleene–Brouwer order is itself a well- ordering if and only if the tree has no infinite branch.

Full-page 1907 colour plate of types of fish to buy from the fishmonger: red mullet, grayling, John Dory, mackerel, cod, whiting, salmon, herring, plaice, flounder, gurnet, crayfish The preface sets out the book's goal of providing "men" with such well-cooked food at home that it may compete with what they could eat "at their clubs, well-ordered taverns, and dining-houses". Mrs. Beeton claims that: She explains that she was thus attempting to make the basics of cookery "intelligible" to any "housewife". The first chapter sets the tone of the book with a quotation from the Book of Proverbs, and in early editions cites also The Vicar of Wakefield with:Beeton. "The Mistress".

The National Equal Rights League (NERL) is the oldest nationwide human rights organization founded in Syracuse, New York in 1864 dedicated to the liberation of black people in the United States. Its origins can be traced back to the emancipation of slaves in the British West Indies in 1833. The league emphasized moral reform and self-help, aiming "to encourage sound morality, education, temperance, frugality, industry, and promote everything that pertains to a well-ordered and dignified life." Black leaders formed state and local branches of the league which drew many members, which caused the society to grow quickly, in areas such as Harrisburg, Pennsylvania, where people such as Thomas Morris Chester joined.

Socrates does not include justice as a virtue within the city, suggesting that justice does not exist within the human soul either, rather it is the result of a "well ordered" soul. A result of this conception of justice separates people into three types; that of the soldier, that of the producer, and that of a ruler. If a ruler can create just laws, and if the warriors can carry out the orders of the rulers, and if the producers can obey this authority, then a society will be just. The city is challenged by Adeimantus and Glaucon throughout its development: Adeimantus cannot find happiness in the city, and Glaucon cannot find honor and glory.

Socrates never positively states what justice is in the human soul/city; it appears he has created a city where justice is not found, but can be lost. It is as though in a well-ordered state, justice is not even needed, since the community satisfies the needs of humans. In terms of why it is best to be just rather than unjust for the individual, Plato prepares an answer in Book IX consisting of three main arguments. Plato says that a tyrant's nature will leave him with "horrid pains and pangs" and that the typical tyrant engages in a lifestyle that will be physically and mentally exacting on such a ruler.

This variant of the lexicographical order is sometimes called shortlex order. In lexicographical order, the word "Thomas" appears before "Thompson" because they first differ at the fifth letter ('a' and 'p'), and letter 'a' comes before the letter 'p' in the alphabet. Because it is the first difference, in this case the 5th letter is the "most significant difference" for alphabetical ordering. An important property of the lexicographical order is that for each , the set of words of length is well- ordered by the lexicographical order (provided the alphabet is finite); that is, every decreasing sequence of words of length is finite (or equivalently, every non-empty subset has a least element).

Pro-slavery advocates claimed that enslaved Africans were lesser human beings who benefited from their bondage. Wilberforce, the Clapham Sect and others were anxious to demonstrate that Africans, and particularly freed slaves, had human and economic abilities beyond the slave trade, and that they were capable of sustaining a well- ordered society, trade and cultivation. Inspired in part by the utopian vision of Granville Sharp, they became involved in the establishment in 1792 of a free colony in Sierra Leone with black settlers from Britain, Nova Scotia and Jamaica, as well as native Africans and some whites. They formed the Sierra Leone Company, with Wilberforce subscribing liberally to the project in money and time.

But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction (C) Berry's Paradox with letters instead of syllables is often related to the set of all natural numbers which can be defined by less than 100 (or any other large number) letters. As the natural numbers are a well- ordered set there must be the least number which cannot be defined by less than 100 letters. But this number was just defined by 65 letters including spaces. (D) König's Paradox was also published in 1905 by Julius König.

In > the VLIW mode, the processor always fetched two instructions and assumed > that one was an integer instruction and the other floating-point. The i860's VLIW mode was used extensively in embedded digital signal processor (DSP) applications since the application execution and datasets were simple, well ordered and predictable, allowing designers to fully exploit the parallel execution advantages enabled by VLIW. In VLIW mode, the i860 could maintain floating-point performance in the range of 20-40 double-precision MFLOPS; a very high value for its time and for a processor running at 25-50Mhz. In the 1990s, Hewlett-Packard researched this problem as a side effect of ongoing work on their PA-RISC processor family.

We see for the first time a woman, the famous Trotula de Ruggiero, who ascends to the honors of the chair, and gives instructions to women in labor. At the beginning of 1000 A.D. in Salerno there was a well-ordered school or society which arose by practitioners of medical disciplines. The first constitution of the Societas was formed by those jatrophysici, who took office on the hill Bonae diei and Salernitam Scholam scripsere, laid the foundations of that school and leaving to posterity the Flos Medicinae, a monument of greatness and piety. The teaching of medicine in Salerno in the Middle Ages was carried out by private professors whose name was assigned to doctors.

The establishment and integration of varied Christian ideas and Christianity-related notions, including diverse topics and themes of the Bible, in a single, coherent and well-ordered presentation is a relatively late development. In Eastern Orthodoxy, an early example is provided by John of Damascus's 8th-century Exposition of the Orthodox Faith, in which he attempts to set in order and demonstrate the coherence of the theology of the classic texts of the Eastern theological tradition. In the West, Peter Lombard's 12th-century Sentences, wherein he thematically collected a great series of quotations of the Church Fathers, became the basis of a medieval scholastic tradition of thematic commentary and explanation. Thomas Aquinas's Summa Theologiae best exemplifies this scholastic tradition.

It was a well-ordered establishment comprising a main house, three out houses, stable, cow yard, a formally laid out garden with pathways, and front fencing. To the northwest of the government residence, outside what is now Friend Park, an old brick shed was identified, and further to the northwest, overlooking Barney Point Beach, was the house of the Clerk of Petty Sessions. To the southwest was a more extensive garden and stock yard, which appear to have been associated with the government residence. No graves were identified on the plan. On 11 July 1862 Surveyor Permien completed a survey of sections 55 to 86 of the Town of Gladstone (survey plan G14.7).

Gantt returned home and for a time officiated in his native parish, Christ Church, Calvert County. On January 28, 1776 he began to preach at All Hallow’s Parish in Worcester County. Four years later he became rector of his native parish, and sustained himself by practicing medicine. In 1795 Gantt moved to Georgetown in the District of Columbia. His work in Washington continued to combine ministry and medicine as indicated by an invoice in the White House Historical Association's archives; the doctor’s bill for President Thomas Jefferson’s household dated March 22, 1802, lists the medical services provided to several servants by Dr. Edward Gantt.“A Well-Ordered Household”: Domestic Servants in Jefferson’s White House, by Lucia Stanton, p. 11.

The Four Doctors of the Western Church, Saint Augustine of Hippo (354–430), Gerard Seghers Saint Augustine offered a version of divine command theory that began by casting ethics as the pursuit of the supreme good, which delivers human happiness. He argued that to achieve this happiness, humans must love objects that are worthy of human love in the correct manner; this requires humans to love God, which then allows them to correctly love that which is worthy of being loved. Augustine's ethics proposed that the act of loving God enables humans to properly orient their loves, leading to human happiness and fulfilment. Augustine supported Plato's view that a well-ordered soul is a desirable consequence of morality.

In computing, as well as in non-computing contexts, a file sequence is a well- ordered, (finite) collection of files, usually related to each other in some way. In computing, file sequences should ideally obey some kind of locality of reference principle, so that not only all the files belonging to the same sequence ought to be locally referenced to each other, but they also obey that as much as is their proximity with respect to the ordering relation. Explicit file sequences are, in fact, sequences whose filenames all end with a numeric or alphanumeric tag in the end (excluding file extension). The aforementioned locality of reference usually pertains either to the data, the metadata (e.g.

Seeing the well-ordered community where people have learned to make everything they need themselves, Simon begins to feel that his own people are "failures", having tried to restore pre-war standards at the expense of their children's futures. Simon meets Catherine, now known as "Blind Kate," blind after years of exposure to ultraviolet radiation and covered in festering sores. Simon sees in her a glimpse of his own future and, on learning that she is Laura's grandmother, is so repulsed at the thought of being related to a mutant that he can not bring himself to acknowledge it. Instead, when Laura asks if he has ever heard of the people who once came to the community to take the cattle, he claims not to know them.

The explorer John Speke, searching for the source of the Nile, had visited Buganda in the 1860s and back home in Britain given a glowing account of the advanced Bantu kingdom he had found in East Africa, and fellow explorers as well as colonialists were to soon follow him into the kingdom. The journalist Henry Morton Stanley visited Buganda in 1875 and painted a good picture of the kingdom's strength, as well as providing an estimate of Buganda troop strength. At Buganda's capital, Stanley found a well-ordered town of about 80,000 surrounding the king's palace, which was situated atop a commanding hill. A wall more than four kilometers in circumference surrounded the palace compound, which was filled with grass-roofed houses, meeting halls, and storage buildings.

P-A-X-497/341 (aka Pax), a curious human from a well-ordered but loveless year 3127, travels back in time to the year 2011 to satisfy his curiosity about such archaic concepts as love, passion and sex, after finding a book by newly published romance novelist Elizabeth Barrett, who also works at a newspaper that deals in primarily made up stories. He is told that love caused people to act strangely and was one of the root causes for suffering in the world. He decided to go back to the year 2011 to figure what love is. He winds up making his own discoveries when he meets Elizabeth, who turns out to be the woman of his dreams.

65 Crooke denied all the charges, and by now he had gained the goodwill of most of the influential men in Munster, including William Lyon, Bishop of Cork, Richard Boyle, 1st Earl of Cork, and Henry Danvers, 1st Earl of Danby, Lord President of Munster. His friends spoke up for him: Bishop Lyon in particular praised his extraordinary achievement in having created a well-ordered town out of nothing in less than 5 years. The Privy Council, despite an apparent preliminary finding that he was guilty, in the end exonerated Crooke completely, but not everyone was satisfied: the authorities in Venice continued to call Baltimore "a nest of pirates", and it was claimed that the entire population of the town were implicated in the illicit business.Hanna p.

As a sports governing body seeking to control and integrate all sport activities in Germany, the DRL/NSRL provided a highly organized structure. This structuralization, whose nationalistic seriousness was often outright theatrical, was in line with the Nazi Party's goal of reminding Germans constantly that they were members of a large extended country. According to Paragraph 2 of the DRL's Statutes: The purpose of the League of the Reich for Physical Exercise is the training of the body and character of Germans grouped together in member organizations through planned physical exercises and care of the national conscience (Volksbewußtsein) in the spirit of the National Socialist state. Regarding method and purpose, and keeping aside the ideology, the well-ordered and solemn DRL/NSRL system proved itself efficient.

An attempt by Charles to impose his authority by military means led to the 1639 and 1640 Bishop's Wars, which left the Covenanters in control of Scotland. When the First English Civil War began in 1642, the Scots remained neutral at first but sent troops to Ulster to support their co-religionists in the Irish Rebellion; the bitterness of this conflict radicalised views in Scotland and Ireland. Since Calvinists believed a 'well-ordered' monarchy was part of God's plan, the vast majority of Covenanters agreed monarchy itself was divinely ordered but disagreed on who held ultimate authority in clerical affairs. Scottish Royalists tended to be 'traditionalists' in religion and politics, but there were many other factors, including nationalist allegiance to the kirk.

In one respect 'Abd-al- Hamad's exposition is more thorough than that of al-Khwarizmi for he gives geometric figures to prove that if the discriminant is negative, a quadratic equation has no solution. Similarities in the works of the two men and the systematic organization found in them seem to indicate that algebra in their day was not so recent a development as has usually been assumed. When textbooks with a conventional and well-ordered exposition appear simultaneously, a subject is likely to be considerably beyond the formative stage. [...] Note the omission of Diophantus and Pappus, authors who evidently were not at first known in Arabia, although the Diophantine Arithmetica became familiar before the end of the tenth century.

Hospitals and healthcare services are vital components of any well-ordered and humane society, and will indisputably be the recipients of societal resources. That hospitals should be places of safety, not only for patients but also for the staff and for the general public, is of the greatest importance. Quality of hospitals and healthcare services is also of great interest to many other bodies, including governments, NGOs targeting healthcare and social welfare, professional organisations representing doctors, patient organisations, shareholders of companies providing healthcare services, etc. However, accreditation schemes are not the same thing as government-controlled initiatives set up to assess healthcare providers with only governmental objectives in mind - ideally, the functioning and finance of hospital accreditation schemes should be independent of governmental control.

Strachan was a leader of anti-American elements, which he saw as a republican and democratic threat that promised chaos and an end to a well- ordered society. Strachan invented the "militia myth" to the effect that the local militia had done more to defend Canada than the British Army, which has been rejected by Canadian historians. Strachan supported a strict interpretation of the Constitutional Act of 1791, claiming that clergy reserves were to be given to the Church of England alone, rather than to Protestants in general. In 1826, his interpretation was opposed by Egerton Ryerson, who advocated the separation of church and state and argued that the reserves should be sold for the benefit of education in the province.

As a product of a devout religious upbringing, Lewis was critical of the Charles Darwin's theory of evolution for much of her life, instead positing that God was responsible for an intricate and well ordered universe. Only in the 1890s did Lewis come to accept some evolutionary ideas, still seeing the process as part and parcel of a grand theist system. Lewis particularly rejected Darwin's idea that random variation was part of the process behind natural selection, arguing instead that evolution was a divinely directed process for the perfection of supernaturally created species. Held back by her theistic determinism and lack of higher education, Lewis was forced to limit herself to popular lectures on the naturalism to work as a freelance scientific illustrator, by which she made her living.

When the Prussians arrived and attacked the French right flank in ever-increasing numbers, Napoleon's strategy of keeping the coalition armies divided had failed and a combined coalition general advance drove his army from the field in confusion. Grouchy organised a successful and well-ordered retreat towards Paris, where Marshal Davout had 117,000 men ready to turn back the 116,000 men of Blücher and Wellington. General Vandamme was defeated at the Battle of Issy and negotiations for surrender had begun. The charge of the French Cuirassiers at the Battle of Waterloo against a square of Scottish Highlanders On arriving at Paris three days after Waterloo, Napoleon still clung to the hope of a concerted national resistance; but the temper of the legislative chambers, and of the public generally, did not favour his view.

A pause in the battle at dusk (approximately 20:20 to 21:10) allowed Derfflinger and the other German battlecruisers to cut away wreckage that interfered with the main guns, extinguish fires, repair the fire control and signal equipment, and prepare the searchlights for nighttime action. During this period, the German fleet reorganized into a well-ordered formation in reverse order, when the German light forces encountered the British screen shortly after 21:00. The renewed gunfire gained Beatty's attention, so he turned his battlecruisers westward. At 21:09, he sighted the German battlecruisers, and drew to within before opening fire at 21:20. In the ensuing melee, Derfflinger was hit several times; at 21:34, a heavy shell struck her last operational gun turret and put it out of action.

Learning of an armored German advance from Metković, the Partisans used the demolition points to turn back the German advance. The command of the 26th Division, expecting a counterattack from the Germans at Oštrikovac as well, ordered the 1st Brigade to withdraw to the flanks of the Oštrikovac-Vukov Gorge road and prepared to ambush any advancing German forces. At the same time the 11th Brigade positioned along the Metković-Dubrovnik road to ambush the retreating column from Metković that had been stopped earlier that day. The command of the 26th Division, worried about the uncertainty of the situation in Vukov Gorge and eager to secure its gains (Neum and Ston) earlier that week, had actually ordered the 1st Brigade to withdraw back to Pelješac and the 11th to Neum.

The course of study prescribed by Thomas was elastic and the methods of teaching vary each year according to age, development, tastes and interest of the pupils. She believed that "what we teach has higher ends than merely being taught and learned," and held that the supreme end of education was the formation of character, therefore all subjects were dealt with vitally and with relation to the life of the individual pupil, whose sense of responsibility was thus awakened and gradually developed so that the foundation was laid upon which to build a future, well-ordered, satisfying life. Thomas laid much stress upon the moral as well as the religious training of the girls under her care. Right thinking as well as right living was the basic principle of character building.

He began by postulating -- "The principle of non-derogation is however based upon the presumed intention of the parties. The rights derived from the principle must have a consensual origin."Lord Hoffman's postulate, however, simply refuses to accept Lord Templeman's clearly expressed concept that any intention not to derogate from a grant is constructive, that is to say that it is implied by law irrespective of the actual wishes of the grantor, because perceived considerations of public policy require that certain consequences shall follow from certain transactions in order that society shall operate in accordance with what Lord Templeman considered necessary to the operation of a well-ordered State. In short, Lord Hoffman did not agree with Lord Templeman's unarticulated hierarchy of values, nor did he articulate his own.

An infinite set can simply be defined as one having the same size as at least one of its proper parts; this notion of infinity is called Dedekind infinite. The diagram to the right gives an example: viewing lines as infinite sets of points, the left half of the lower blue line can be mapped in a one-to-one manner (green correspondences) to the higher blue line, and, in turn, to the whole lower blue line (red correspondences); therefore the whole lower blue line and its left half have the same cardinality, i.e. "size". Cantor defined two kinds of infinite numbers: ordinal numbers and cardinal numbers. Ordinal numbers characterize well-ordered sets, or counting carried on to any stopping point, including points after an infinite number have already been counted.

The version of the paradox above is anachronistic, because it presupposes the definition of the ordinals due to John von Neumann, under which each ordinal is the set of all preceding ordinals, which was not known at the time the paradox was framed by Burali-Forti. Here is an account with fewer presuppositions: suppose that we associate with each well-ordering an object called its order type in an unspecified way (the order types are the ordinal numbers). The order types (ordinal numbers) themselves are well- ordered in a natural way, and this well-ordering must have an order type \Omega. It is easily shown in naïve set theory (and remains true in ZFC but not in New Foundations) that the order type of all ordinal numbers less than a fixed \alpha is \alpha itself.

Any ordinal number can be made into a topological space by endowing it with the order topology (since, being well-ordered, an ordinal is in particular totally ordered): in the absence of indication to the contrary, it is always that order topology that is meant when an ordinal is thought of as a topological space. (Note that if we are willing to accept a proper class as a topological space, then the class of all ordinals is also a topological space for the order topology.) The set of limit points of an ordinal α is precisely the set of limit ordinals less than α. Successor ordinals (and zero) less than α are isolated points in α. In particular, the finite ordinals and ω are discrete topological spaces, and no ordinal beyond that is discrete.

Some businesses have taken off and had success in this market with healthy foods and due to many health concerns and fast food stereotypes, it is emerging as an expected thing. According to Jason Daley, healthful fast food takeoff is explained by the fact that it has "ceased to be a thing-now, it's simply expected." In other parts of the world, American and American-style fast food outlets have been popular for their quality, customer service, and novelty, even though they are often the targets of popular anger towards American foreign policy or globalization more generally. Many consumers nonetheless see them as symbols of the wealth, progress, and well-ordered openness of Western society and they therefore become trendy attractions in many cities around the world, particularly among younger people with more varied tastes.

He related that his ancestors came from Wales to America in the early 17th century and settled in the western frontier of the Virginia colony, which influenced his zeal for individual and state rights. Jefferson described his father as uneducated, but with a "strong mind and sound judgement". His enrollment in the College of William and Mary and election to the Continental Congress in Philadelphia in 1775 were included. He also expressed opposition to the idea of a privileged aristocracy made up of large landowning families partial to the King, and instead promoted "the aristocracy of virtue and talent, which nature has wisely provided for the direction of the interests of society, & scattered with equal hand through all its conditions, was deemed essential to a well-ordered republic".

These towers are the oldest remaining part of any Anglican church in Australia. The erection of the extant towers was a significant element of Governor Macquarie's programme of fostering religion and education as well as his desire to make Parramatta (the second mainland settlement of the colony and the site of his second Government House) into a tidy, well-ordered settlement. Surviving views and vistas of St Johns Cathedral have state historical significance. These include: east along Hunter Street to the Cathedral towers; east from Hunter Street across the northern Cathedral grounds towards the Town Hall and the site of the Governor's annual "feast" with Aboriginal clans (instituted by Governor Macquarie) that took place at the rear (eastern end) of the Cathedral, and views from Church Street towards St John's Cathedral.

In the 1950s Bindi lived in the Pindan Cooperative settlement in Port Hedland, a well-ordered collective and one of the first Aboriginal cooperatives formed in Western Australia, where residents worked in the mining industry and received equal pay. In October 1959 she successfully lobbied for a school for Pindan while in Perth to be fitted for an artificial limb after losing her leg in an accident in the bush. In Perth she also spoke at meetings of the Western Australian branch of the Union of Australian Women, a group which supported the cause of Aboriginal rights. In 1960 the Cooperative split into some who wished to continue with McLeod, and others who thought that his position against mining interests were counterproductive to the Aboriginal cause, which included Bindi.

Instead, spinning was a communal activity, frequently performed in a ' (spinning room), a place where women most likely kept the oral traditions alive by telling stories while engaged in tedious work. In the stories, a woman's personality is often represented by her attitude toward spinning; a wise woman might be a spinster and Bottigheimer explains that the spindle was the symbol of a "diligent, well-ordered womanhood." In some stories, such as "Rumpelstiltskin", spinning is associated with a threat; in others, spinning might be avoided by a character who is either too lazy or not accustomed to spinning because of her high social status. The tales were also criticized for being insufficiently German, which influenced the tales that the brothers included as well as their use of language.

Although there were passing comments on international affairs in A Theory of Justice, it was not until late in his career that Rawls formulated a comprehensive theory of international politics with the publication of The Law of Peoples. He claimed there that "well-ordered" peoples could be either "liberal" or "decent." Rawls's basic distinction in international politics is that his preferred emphasis on a society of peoples is separate from the more conventional and historical discussion of international politics as based on relationships between states. Rawls argued that the legitimacy of a liberal international order is contingent on tolerating decent peoples, which differ from liberal peoples, among other ways, in that they might have state religions and deny adherents of minority faiths the right to hold positions of power within the state, and might organize political participation via consultation hierarchies rather than elections.

Henty defends slavery throughout the novel, stating although slavery was capable of "abominable" cruelty under brutal masters, "..taken all in all, the negroes on a well-ordered estate, under kind masters, were probably a happier class of people than the laborers upon any estate in Europe." Chapter I, "A Virginian Plantation", With Lee in Virginia, Wildside Press LLC (Reprint) 2007 (p.10) At the novel's end, Henty has the Wingfield family's former slaves return and continue working for their former owners: > The negroes, however, for the most part remained steadily working on the > estate. A few wandered away, but their places were easily filled; for the > majority of the freed slaves very soon discovered that their lot was a far > harder one than it had been before, and that freedom so suddenly given was a > curse rather than a blessing to them.

He also gradually collected a considerable private library bearing on ecclesiastical questions, while he made notes from daily papers and from other publications for his own instruction. The subsequent arrangement of these notes in order suggested to him the idea of turning his labours to the benefit of the public, an idea which he realized in the Dictionary, a mine of interesting data and authoritative in matters concerning the Pontifical Court, the organization of the Curia and the Church, and the administration of the Papal States. In matters of history, it depends on the writers whom its author consulted. It is, however, not a well-ordered or homogeneous work, but these defects may be readily forgiven in view of the fact that its author did his work alone, without real collaboration, and wrote at times sixteen hours a day.

When the Spanish adopted the colunella (the first of the mixed pike and shot formations), they used small groups of sword and buckler men to break the deadlock of the push of pike, as the Swiss and Germans used halberdiers, comparable to the role of the German Doppelsöldner during the same period. At the Battle of Ravenna in 1512, they proved to be very effective with this tactic; however, when facing a fresh, well ordered pike square, they were vulnerable, as at the Battle of Seminara. They were also very vulnerable to attack by cavalry. As battlefield tactics evolved during the early 16th century, the Spanish ultimately concluded that the vulnerability of the rodeleros on the battlefield outweighed their strengths, and they were dropped as a troop type when the Spanish infantry were reorganized into tercios in the 1530s.

There are a number of listed buildings in the village, including Manor Farmhouse, with three bays and two storeys, built in the early nineteenth century, and Binge Farmhouse, with five bays and two storeys, together with a basement and garret, built in the middle eighteenth century. Willow Tree Cottage is a single-storeyed eighteenth-century building with three bays and an attic, while Willow Tree Farmhouse is an L-shaped building, consisting of a seventeenth-century gable- ended wing and a nineteenth-century wing. As a result of the influence of the enclosure movement, the village prospered, and this is reflected in the substantial farmhouses and the well-ordered field system surrounding the village. Laneham was enclosed by Act of Parliament in 1772, the 12th year of George III's reign; the enclosure involved 1,073 of the parish's .

The general name of mnemonics, or memoria technica, was the name applied to devices for aiding the memory, to enable the mind to reproduce a relatively unfamiliar idea, and especially a series of dissociated ideas, by connecting it, or them, in some artificial whole, the parts of which are mutually suggestive. Mnemonic devices were much cultivated by Greek sophists and philosophers and are frequently referred to by Plato and Aristotle. In later times the poet Simonides was credited for development of these techniques, perhaps for no reason other than that the power of his memory was famous. Cicero, who attaches considerable importance to the art, but more to the principle of order as the best help to memory, speaks of Carneades (perhaps Charmades) of Athens and Metrodorus of Scepsis as distinguished examples of people who used well-ordered images to aid the memory.

Instead writing in the United States quickly returned to its realist orthodoxy and the term irrealism fell into disuse. In recent years, however, the term has been revived in an attempt to describe and categorize, in literary and philosophical terms, how it is that the work of an irrealist writer differs from the work of writers in other, non-realistic genres (e.g., the fantasy of J.R.R. Tolkien, the magical realism of Gabriel García Márquez) and what the significance of this difference is. This can be seen in Dean Swinford's essay Defining irrealism: scientific development and allegorical possibility. Approaching the issue from a structuralist and narratological point of view, he has defined irrealism as a "peculiar mode of postmodern allegory" that has resulted from modernity’s fragmentation and dismantling of the well-ordered and coherent medieval system of symbol and allegory.

Since the cardinal numbers are well-ordered by indexing with the ordinal numbers (see Cardinal number, formal definition), this also establishes that there is no greatest ordinal number; conversely, the latter statement implies Cantor's paradox. By applying this indexing to the Burali-Forti paradox we obtain another proof that the cardinal numbers are a proper class rather than a set, and (at least in ZFC or in von Neumann–Bernays–Gödel set theory) it follows from this that there is a bijection between the class of cardinals and the class of all sets. Since every set is a subset of this latter class, and every cardinality is the cardinality of a set (by definition!) this intuitively means that the "cardinality" of the collection of cardinals is greater than the cardinality of any set: it is more infinite than any true infinity. This is the paradoxical nature of Cantor's "paradox".

Any well-ordered set is similar (order-isomorphic) to a unique ordinal number \alpha; in other words, its elements can be indexed in increasing fashion by the ordinals less than \alpha. This applies, in particular, to any set of ordinals: any set of ordinals is naturally indexed by the ordinals less than some \alpha. The same holds, with a slight modification, for classes of ordinals (a collection of ordinals, possibly too large to form a set, defined by some property): any class of ordinals can be indexed by ordinals (and, when the class is unbounded in the class of all ordinals, this puts it in class-bijection with the class of all ordinals). So the \gamma-th element in the class (with the convention that the "0-th" is the smallest, the "1-st" is the next smallest, and so on) can be freely spoken of.

Jácome de Bruges, 1st Captain-Donee of Terceira (born Jacob van Brugge, Gruuthuse en van der Aa in 1418 in Bruges, Flanders) was the older brother of Louis de Gruuthuse, 1st Earl of Winchester of the wealthy Gruuthuse noble family from Bruges, their grandfather Jean III d'Aa of Gruuthuse participated in the great tournament of Bruges on 11 March, 1393. Jácome became a servant of Prince Henry the Navigator of Portugal (the son of king John I), who initiated the so-called Portuguese Age of Discovery in the 15th century. As a native of a city belonging to the Hanseatic league, Jácome de Bruges had been exposed to well-ordered mercantilism, and he understood the value of international trade as a driver of national prosperity. Consequently, he was a logical candidate to enter into the service of the like-minded Prince Henry in Portugal.

HM Prison Cardiff in 2010 The prisons in Wales are run by Her Majesty's Prison Service, which is in turn a part of HM Prison and Probation Service (HMPPS) which is an executive agency of the Ministry of Justice responsible for the correctional services in England and Wales. The objectives of prison confinement in Wales is threefold: to "hold prisoners securely", to "reduce the risk of prisoners re-offending" and to "provide safe and well-ordered establishments in which we treat prisoners humanely, decently and lawfully". Although the concept of incarceration as a punishment for wrongdoing did not exist in Wales, as in the rest of Britain, during the medieval period, from Tudor times onwards correction houses began appearing throughout the country. In the 18th century several buildings began taking on the function of modern prisons, and in 1878 Welsh prisons came under centralised government control.

The work, then, of St. Gregory was a musical cento, a compilation (centonem ... compilavit) of pre-existing material into a coherent and well-ordered whole. This does not necessarily imply that the musical centonization of the melodies was the special and original work of the Saint, as the practice of constructing new melodies from separate portions of older ones had already been in vogue two or three centuries earlier than his day. But is it clear that the cento was one of melodies as well as of texts? In answer it might indeed by said that in the earliest ages of the Church the chants must have been so very simple in form that they could easily be committed to memory; and that most of the subsequently developed antiphonal melodies could be reduced to a much smaller number of types, or typical melodies, and could thus also be memorized.

The Lord of Chicha's court was so opulent, even more than Atahualpa's, that the Spanish, most of them who did not meet Atahualpa until then, at first thought the Lord of Chicha was the Inca Emperor. Pizarro and his 168 soldiers met Atahualpa in the Cajamarca plaza after weeks of marching from Piura. The Spanish Conquistadors and their Indian allies captured Atahualpa in the Battle of Cajamarca, where they also massacred several thousand unarmed Inca civilians and soldiers in an audacious surprise attack of cannon, cavalry, lances and swords. The rest of the army of 40,000–80,000 (Conquistadors' estimates) was stationed some kilometers away from Cajamarca in a large military camp, near the Inca resort town of Pultamarca (currently known as "Baños del Inca"), with its thousands of tents as looking from afar "like a very beautiful and well-ordered city, because everyone had his own tent".

" He characterized "promiscuity, perversion, sadism, and irregular practices" as well as "free love, easy marriage and quick divorce" as being undesirable activities, "since it is non- survival not to have a well ordered system for the creation and upbringing of children, by families." Such "sexual perverts" engaged in "irregular practices which do anything but tend toward the creation of children" and "efforts [which] tend not towards enjoyment but toward the pollution and derangement of sex itself so as to make it as repulsive as possible to others and so to inhibit procreation." Hubbard's 1951 book Handbook for Preclears likewise classified homosexuality as "about 1.1 (covert hostility) on the tone scale", along with "general promiscuity". He set out what he saw as the cause of homosexuality: a mental "aberration", with the result that "an individual aberrated enough about sex will do strange things to be a cause or an effect.

In the mathematical field of group theory, a subgroup H of a given group G is a serial subgroup of G if there is a chain C of subgroups of G extending from H to G such that for consecutive subgroups X and Y in C, X is a normal subgroup of Y. The relation is written H ser G or H is serial in G. If the chain is finite between H and G, then H is a subnormal subgroup of G. Then every subnormal subgroup of G is serial. If the chain C is well-ordered and ascending, then H is an ascendant subgroup of G; if descending, then H is a descendant subgroup of G. If G is a locally finite group, then the set of all serial subgroups of G form a complete sublattice in the lattice of all normal subgroups of G.

The inscription „Eigenthum der deutschen Nation“ ("Property of the German Nation") at the main entrance was installed when the museum was founded in 1852, and was commissioned by Hans von und zu Aufseß The Germanisches Museum, as it was named initially, was founded by a group of individuals led by the Franconian baron Hans von und zu Aufsess, whose goal was to assemble a "well-ordered compendium of all available source material for German history, literature and art". The term Germanic should be understood in the historical context of the mid nineteenth century. In 1846, German linguists and historians, amongst them the Brothers Grimm, Leopold Ranke und Jacob Burckhardt, had met in Frankfurt, and decided to use "Germanistik" as a comprehensive term embracing all the fields of their academic disciplines related to the culture of German speaking regions. The German revolutions of 1848–49 had failed to achieve a liberalised and unified Germany.

The riots initiated by Jenny Geddes in St Giles Cathedral led to the Bishops' Wars James claimed his authority as monarch and head of the kirk came from God; when he also became King of England in 1603, a unified Church of Scotland and England governed by bishops became the first step in his vision of a centralised, Unionist state. Although both were nominally Episcopalian, they were very different in governance and doctrine; Scottish bishops were doctrinal Calvinists who viewed many Church of England practices as little better than Catholicism. Since Calvinists believed a 'well-ordered' monarchy was part of God's plan, the vast majority of Scots agreed monarchy itself was divinely ordered but disagreed on who held ultimate authority in clerical affairs. The Covenanter view was summarised by Andrew Melville as '...Thair is twa Kings and twa Kingdomes in Scotland... Chryst Jesus the King and this Kingdome the Kirk, whose subject King James the Saxt is.

In the case of neoliberal governmentality (a kind of governmentality based on the predominance of market mechanisms and of the restriction of the action of the state) the knowledge produced allows the construction of auto-regulated or auto-correcting selves. In his lecture titled Governmentality, Foucault gives us a definition of governmentality: As Foucault's explicit definition is rather broad, perhaps further examination of this definition would be useful. We shall begin with a closer inspection of the first part of Foucault's definition of governmentality: This strand of the three-part definition states that governmentality is, in other words, all of the components that make up a government that has as its end the maintenance of a well-ordered and happy society (population). The government's means to this end is its "apparatuses of security," that is to say, the techniques it uses to provide this society a feeling of economic, political, and cultural well-being.

In ZFC, the order type of a well- ordering W is then defined as the unique von Neumann ordinal which is equinumerous with the field of W and membership on which is isomorphic to the strict well-ordering associated with W. (the equinumerousness condition distinguishes between well-orderings with fields of size 0 and 1, whose associated strict well-orderings are indistinguishable). In ZFC there cannot be a set of all ordinals. In fact, the von Neumann ordinals are an inconsistent totality in any set theory: it can be shown with modest set theoretical assumptions that every element of a von Neumann ordinal is a von Neumann ordinal and the von Neumann ordinals are strictly well-ordered by membership. It follows that the class of von Neumann ordinals would be a von Neumann ordinal if it were a set: but it would then be an element of itself, which contradicts the fact that membership is a strict well-ordering of the von Neumann ordinals.

Whereas for many corseting was accepted as necessary for beauty, health, and an upright military-style posture, dress reformists viewed tightlacing as vain and, especially at the height of the era of Victorian morality, a sign of moral indecency. American women active in the anti-slavery and temperance movements, with experience in public speaking and political agitation, demanded sensible clothing that would not restrict their movement. While support for fashionable dress contested that corsets maintained an upright, ‘good figure’, as a necessary physical structure for moral and well-ordered society, these dress reformists contested that women’s fashions were not only physically detrimental but “the results of male conspiracy to make women subservient by cultivating them in slave psychology.” They believed a change in fashions could change the whole position of women, allowing for greater social mobility, independence from men and marriage, the ability to work for wages, as well as physical movement and comfort.

She had no ambition to propound a theory, or to write her own name on any book, or plant, or opinion. Her delight in books was not tainted by any wish to shine..." Emerson took care to reassure readers that her housework never suffered as a result of her studies: > But this wide and successful study was, during all the hours of middle life, > only the work of hours stolen from sleep, or was combined with some > household task which occupied the hands and left the eyes free. She was > faithful to all the duties of wife and mother in a well-ordered and > eminently hospitable household. George Frisbie Hoar called her "one of the most wonderful scholars of her time, or indeed of any time," and in the same paragraph described her as "simple as a child, an admirable wife and mother, performing perfectly all the commonest duties of the household.

The axioms of NBG with the axiom of replacement replaced by the weaker axiom of separation do not imply the axiom of limitation of size. Define \omega_\alpha as the \alpha-th infinite initial ordinal, which is also the cardinal \aleph_\alpha; numbering starts at 0, so \omega_0 = \omega. In 1939, Gödel pointed out that Lωω, a subset of the constructible universe, is a model of ZFC with replacement replaced by separation.. To expand it into a model of NBG with replacement replaced by separation, let its classes be the sets of Lωω+1, which are the constructible subsets of Lωω. This model satisfies NBG's class existence axioms because restricting the set variables of these axioms to Lωω produces instances of the axiom of separation, which holds in L. It satisfies the axiom of global choice because there is a function belonging to Lωω+1 that maps ωω onto Lωω, which implies that Lωω is well-ordered.

Establishment of economic foundation for democracy. Over successive Economic Summits, this economic philosophy formed the basis of reform proposals culminating in several National Development Agendas. By NES#3 (1996), the National Stakeholder Consensus was that there was a need for a National Vision. This Summit proposed a National Vision Statement for Nigeria by 2025: “Nigeria will be a well ordered, well-governed, just and prosperous nation, united in a sustained endeavor”. It also proposed a 'Change Program' from 1996 to 2010, laying the foundation for the 'Vision 2010' agenda. Following the extensive recommendations of the NES#3, Nigeria's 'Vision 2010' Committee, consisting of 240 members who were primarily from the NESG, submitted the 'Vision 2010' report; hence NES#4 was dedicated to its implementation. By 2001, Nigeria had transformed into a modern 21st-Century African Democracy and with a growth rate of 10%. World Bank Reports noted Nigeria in the 'MINT' nations with the economic potential to join the 'BRICS' nations, as well as the top league of 20 most prosperous nations in the world.

Well-founded phenomena (), in the philosophy of Gottfried Leibniz, are ways in which the world falsely appears to us, but which are grounded in the way the world is (as opposed to dreams or hallucinations, which are false appearances that are not thus grounded). For Leibniz, the universe is made up of an infinite number of simple substances or monads, each of which contains a representation of the entire universe (past, present, and future), and which are all causally isolated from one another ("Monads have no windows through which anything could enter or depart."Leibniz, "The Monadology" (1714), §7.) For the most part the monads' perceptions are more or less confused and obscure, but some of them correspond either to the ways in which other monads are related or to the ways that the representation is genuinely ordered; these are the well-founded phenomena. In the world of ordinary experience we might call a rainbow a well-ordered phenomenon; it appears to us to be a coloured arch in the sky, though there is in fact no arch there.

RNase H is located at the beginning of N-terminal and named after the RNase H endoribonuclease family since they share a similar structure; however, RNase H serves as a structural function rather than catalytic function because it is lack of active-site residue. Next, the S1 subdomain and 5’ sensing region are implanted in RNase H fold. The RNase E S1 domain adopts an OB-fold in which flexible loops are attached to a well- ordered five-stranded β-barrel core. In the ribonuclease E, the S1 domain not only aids in the formation of the tetrameric quaternary structure by dimerization but also serves as a substrate-binding site to facilitate RNA hydrolysis by the catalytic domains within this tetrameric enzyme. With S1 subdomain, 5’ sensing region functions as a substrate-binding site that helps to stabilize the target RNA molecule on one subunit so that the other subunit within a dimer can cleave the RNA of interest. The 5’ sensing region located at a distance from the catalytic site, which resides on the DNase I subdomain.

Justice John Marshall Harlan delivered the decision for a 7–2 majority that the Massachusetts law did not violate the Fourteenth Amendment. The Court held that "in every well ordered society charged with the duty of conserving the safety of its members the rights of the individual in respect of his liberty may at times, under the pressure of great dangers, be subjected to such restraint, to be enforced by reasonable regulations, as the safety of the general public may demand" and that "[r]eal liberty for all could not exist under the operation of a principle which recognizes the right of each individual person to use his own, whether in respect of his person or his property, regardless of the injury that may be done to others." Furthermore, the Court held that mandatory vaccinations are not arbitrary or oppressive so long as they do not "go so far beyond what was reasonably required for the safety of the public". In Massachusetts, with smallpox being "prevalent and increasing in Cambridge", the regulation in question was "necessary in order to protect the public health and secure the public safety".

Whereas for many corseting was accepted as necessary for beauty, health, and an upright military-style posture, dress reformists viewed tightlacing as vain and, especially at the height of the era of Victorian morality, a sign of moral indecency. American women active in the anti-slavery and temperance movements, with experience in public speaking and political agitation demanded sensible clothing that would not restrict their movement. While support for fashionable dress contested that corsets maintained an upright, ‘good figure’, as a necessary physical structure for moral and well-ordered society, these dress reformists contested that women’s fashions were not only physically detrimental, but “the results of male conspiracy to make women subservient by cultivating them in slave psychology.”“Women's Clothes and Women's Right,” Robert E. Riegel, American Quarterly, 15 (1963): 390 They believed a change in fashions could change the whole position of women, allowing for greater social mobility, independence from men and marriage, the ability to work for wages, as well as physical movement and comfort.“Women's Clothes and Women's Right,” Robert E. Riegel, American Quarterly, 15 (1963): 391 Despite these protests, little changed in restrictive fashion and undergarments by 1900.

1912 Newspaper Article about the Havemeyer Family, the family of George G. Kip's wife Anna Kip was a partner in the law firm DeWitt, Lockman and Kip, based at 88 Nassau Street, for a number of years, along with George Gosman DeWitt and John Thomas Lockman. In 1882 he represented his cousins Robert Goelet and Ogden Goelet (builder of Ochre Court and father of Mary Goelet) before the New York Supreme Court in a legal battle that erupted over control of trusts set up by Peter P. Goelet and Jean B. Goelet for their nephews. Kip's firm was known for its work defending the estates of New York's old Dutch families. In the 1880s, Kip moved his family and servants to Ruremont, an 11-acre country estate on Madison Avenue in Morristown, New Jersey, a street then known as "Millionaires Row." In 1902, the Town and Country Life magazine wrote that Ruremont, “with its smooth lawns and well-ordered gardens and greenhouses,” was “one of the most attractive places in Morristown.” Kip was a member of the exclusive Holland Society of New York, the Saint Nicholas Society of the City of New York, the University Club of New York and The Metropolitan Club.

As an appeal to general revelation, Paul the Apostle (AD 5–67), argues in Romans 1:18–20, that because it has been made plain to all from what has been created in the world, it is obvious that there is a God. Marcus Minucius Felix (c. late 2nd to 3rd century), an Early Christian writer, argued for the existence of God based on the analogy of an ordered house in his The Orders of Minucius Felix: "Supposing you went into a house and found everything neat, orderly and well- kept, surely you would assume it had a master, and one much better than the good things, his belongings; so in this house of the universe, when throughout heaven and earth you see the marks of foresight, order and law, may you not assume that the lord and author of the universe is fairer than the stars themselves or than any portions of the entire world ?" Augustine of Hippo (AD 354–430) in The City of God mentioned the idea that the world's "well-ordered changes and movements", and "the fair appearance of all visible things" was evidence for the world being created, and "that it could not have been created save by God".

Similarly, the set ℤ of integers has the least-upper-bound property; if S is a nonempty subset of ℤ and there is some number n such that every element s of S is less than or equal to n, then there is a least upper bound u for S, an integer that is an upper bound for S and is less than or equal to every other upper bound for S. A well-ordered set also has the least-upper-bound property, and the empty subset has also a least upper bound: the minimum of the whole set. An example of a set that lacks the least-upper-bound property is ℚ, the set of rational numbers. Let S be the set of all rational numbers q such that q2 < 2\. Then S has an upper bound (1000, for example, or 6) but no least upper bound in ℚ: If we suppose p ∈ ℚ is the least upper bound, a contradiction is immediately deduced because between any two reals x and y (including and p) there exists some rational p′, which itself would have to be the least upper bound (if p > ) or a member of S greater than p (if p < ).