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Extended Bolzano Weierstrass Theorem
Journal: International Journal of Science and Research (IJSR) (Vol.9, No. 8)Publication Date: 2020-08-05
Authors : K. L. Kaushik;
Page : 820-822
Keywords : Convergence; Bounded; supremum; Completeness;
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- Extended Bolzano Weierstrass Theorem
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Abstract
In this paper we have proved the Extended Bolzano Weierstrass theorem i. e. Let (an) ∞ n=1 be an bounded sequence. Define the set G = {x ∈R: x less than an for infinitely many terms an} Then ∃ a subsequence (ank) converges to a supremum of the set G.
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Last modified: 2021-06-28 17:10:27