A sequence $\displaystyle (x_n)$ has a Cauchy subsequence if and only if it has a subsequence $\displaystyle (x_n_k)$ for which $\displaystyle d(x_n_k,x_n_{k+1}) < 2^{-k}$

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- Oct 21st 2011, 01:39 PMwopashuicauchy subsequence question
A sequence $\displaystyle (x_n)$ has a Cauchy subsequence if and only if it has a subsequence $\displaystyle (x_n_k)$ for which $\displaystyle d(x_n_k,x_n_{k+1}) < 2^{-k}$

- Oct 21st 2011, 04:25 PMDrexel28Re: cauchy subsequence question