How to use be not equal to in a sentence? Find typical usage patterns (collocations)/phrases/context for "be not equal to" and check conjugation/comparative form for "be not equal to". Mastering all the usages of "be not equal to" from sentence examples published by news publications.
In topology, the cartesian product of topological spaces can be given several different topologies. One of the more obvious choices is the box topology, where a base is given by the Cartesian products of open sets in the component spaces.Willard, 8.2 pp. 52-53, Another possibility is the product topology, where a base is given by the Cartesian products of open sets in the component spaces, only finitely many of which can be not equal to the entire component space.
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Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials. A function may be not equal to the sum of its Taylor series, even if its Taylor series is convergent. A function is analytic at a point if it is equal to the sum of its Taylor series in some open interval (or open disk in the complex plane) containing .
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This is consistent with the known results on rational points, notably Faltings's theorem on subvarieties of abelian varieties. More precisely, let X be a projective variety of general type over a number field k. Let the exceptional set Y be the Zariski closure of the union of the images of all nonconstant holomorphic maps C → X. According to the Green–Griffiths–Lang conjecture, Y should be not equal to X. The strong Lang conjecture predicts that Y is defined over k and that X − Y has only finitely many F-rational points for every finite extension field F of k.Lang (1986), Conjecture 5.8.
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