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Research Paper | Mathematics | India | Volume 9 Issue 8, August 2020 | Popularity: 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
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Dr. K. L. Kaushik, "Extended Bolzano Weierstrass Theorem", International Journal of Science and Research (IJSR), Volume 9 Issue 8, August 2020, pp. 820-822, https://www.ijsr.net/getabstract.php?paperid=SR20815190956, DOI: https://www.doi.org/10.21275/SR20815190956