Monday, February 4, 2019

real analysis - Let (xn) be a monotone sequence and contain a convergent subsequence. Prove that (xn) is convergent.

Let (xn) be a monotone sequence and contain a convergent subsequence. Prove that (xn) is convergent.



I know that by the Bolzano-Weierstrass Theorem, every bounded sequence has a convergent subsequence. But I need some hints as to how to prove the question above. Thanks for your help!

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