ii) Use the Cauchy Criterion (CC) to prove the Bolzano-Weierstrass Theorem (BWT) (i.e. you need to prove that given a bounded sequence {n} using the Cauchy Criterion (CC) you can get a convergent subsequence). This establishes the equivalence between CC and BWT. [Hint: Use the method of the proof of the Bolzano-Weierstrass Theorem to construct a sequence of nested intervals {Ik [ak, bk]}, Ik → 0 and a subsequence nk such that Ink € Ik and prove that {n} is a Cauchy sequence.] =

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A:

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A: