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Research Paper | Mathematics | Volume 9 Issue 8, August 2020 | Pages: 820 - 822 | India
Extended Bolzano Weierstrass Theorem
Abstract: In this paper we have proved the Extended Bolzano Weierstrass theorem i. e. Let (an) ∞ n=1 be an bounded sequence. Deï¬ne 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
How to Cite?: Dr. K. L. Kaushik, "Extended Bolzano Weierstrass Theorem", Volume 9 Issue 8, August 2020, International Journal of Science and Research (IJSR), Pages: 820-822, https://www.ijsr.net/getabstract.php?paperid=SR20815190956, DOI: https://dx.doi.org/10.21275/SR20815190956