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# Cauchy sequence watch

1. 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.

2. What's the definition of a Cauchy sequence? (I know, but I want you to give your definition).
3. 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.
4. (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: ...)

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Updated: August 21, 2007
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