(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose {a_n} is a bounded sequence who's set of all subsequential

limits points is {0,1}. Prove that there exists two subsequences,

such that: one subsequence converges to 1 while the other converges

to 0, and each a_n belongs to exactly one of these subsequences.

2. Relevant equations

3. The attempt at a solution

Well, it's clear that at the limit points 0 and 1; there is a subsequence that that converges to it. I'm not quite sure about how to prove that each a_n belongs to exactly one of these subsequences or how to apply the bounded property of {a_n} into this question.

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# Subsequential limit question

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