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1. Let (X, d) be a metric space and let (Xn) C X be a Cauchy sequence. (a) Suppose some subsequence (In; ) C (Xn)

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1. Let (X, d) be a metric space and let (Xn) C X be a Cauchy sequence. (a) Suppose some subsequence (In; ) C (Xn) converges. Prove that (In) must converge. (b) Why isn't part (a) obvious? In other words, why isn't the answer simply "Because Cauchy sequences converge."

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