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

Every bounded sequence has a convergent subsequence.

2. Relevant equations

Suppose that closed intervals I_0 [itex]\supset[/itex] I_1[itex]\supset[/itex] ... [itex]\supset[/itex] I_m and natural numbers n[itex]_{1}[/itex] < n[itex]_{2}[/itex] <

... < n[itex]_{m}[/itex] have been chosen such that for each 0 [itex]\leq[/itex] k [itex]\leq[/itex] m,

(2)

|I[itex]_{k}[/itex]| = [itex]b-a/2^{k}[/itex], x[itex]_{n}_{k}[/itex][itex]\in[/itex]I[itex]_{k}[/itex]n and x[itex]_{n}[/itex] [itex]\in[/itex] I[itex]_{k}[/itex] for infinitely many n.

3. The attempt at a solution

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# Homework Help: Explanation of the Bolzano-Weierstrass theorem proof

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