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Research Paper | Mathematics | India | Volume 9 Issue 8, August 2020 | Rating: 6.3 / 10
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