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    Real Analysis : Cauchy Sequences

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    Give an example of each of the following or argue that such a request is impossible:
    1) A Cauchy sequence that is not monotone.
    2) A monotone sequence that is not Cauchy.
    3) A Cauchy sequence with a divergent subsequence.
    4) An unbounded sequence containing a subsequence that is Cauchy.

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    Solution Summary

    Cauchy sequences are analyzed. The solution is well presented.