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    I'm not sure how to even begin proving this question, I want to prove the converse to the idea that if a sequence is Cauchy, it's convergent.

    The Question: I want to show that if Xn is a cauchy sequence, then it is bounded.
    I'm given a hint: Fix m=N+1 and use the circle inequality.

    Help on answering this, please?
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    What's the definition of a Cauchy sequence? (I know, but I want you to give your definition).
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    i know that any sequence that is convergent is a cauchy sequence and all the terms will eventually become arbitrarily close to one another. And any cauchy sequence is bounded.
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    (Original post by manga)
    i know that any sequence that is convergent is a cauchy sequence and all the terms will eventually become arbitrarily close to one another. And any cauchy sequence is bounded.
    That's not what I asked. Can you give a formal definition of a Cauchy sequence? (Hint: I would expect it to start something like: \forall \epsilon>0...)
 
 
 
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Updated: August 21, 2007

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