For my practice midterm exam this is a question: State whether the following are true or false AND briefly explain why (or give counterexample):
Statement: Every sequence contains a Cauchy subsequence.
I said this is false because I used the example that the sequence of{x_n} = n is divergent. Therefore a convergent subsequence cannot exist, therefor a Cauchy subsequence cannot exist since all Cauchy sequences are convergent.
Am I right or am I missing/getting mixed up some proper information?