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Math Help - Cauchy sequence w/ unbounded subsequence

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    Cauchy sequence w/ unbounded subsequence

    Cauchy sequence w/ unbounded subsequence.

    Is this possible? If so give an example, otherwise argue how it would be impossible?
    Last edited by mr fantastic; November 13th 2009 at 12:26 PM. Reason: Added title to main body of post
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    Quote Originally Posted by really.smarty View Post
    Cauchy sequence w/ unbounded subsequence.

    Is this possible? If so give an example, otherwise argue how it would be impossible?

    If you mean in the real or complex numbers then no, it's not posible since every Cauchy sequence converges (in fact this is an iff theorem) and is thus bounded.

    Tonio
    Last edited by Plato; November 13th 2009 at 01:37 PM.
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    I think there's different answers to this question depending on whether you are in a metric space but I'll assume not...

    Here's a theorem for you.
    Any Cauchy sequence is bounded.

    Ill post up a proof if you need me to but basically just use the definition of a Cauchy sequence to show it converges.

    Since any Cauchy sequence is bounded, its subsequences must be bounded.
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    thank you!
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