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Research Paper | Mathematics | India | Volume 9 Issue 8, August 2020

Extended Bolzano Weierstrass Theorem

Dr. K. L. Kaushik

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 < an for infinitely many terms an} Then ∃ a subsequence (ank) converges to a supremum of the set G.

Keywords: Convergence, Bounded, supremum, Completeness

Edition: Volume 9 Issue 8, August 2020,

Pages: 820 - 822