Hi I need confirmation, Thank you.

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- Dec 14th 2013, 03:31 AMdavidciprutConfirmation
Hi I need confirmation, Thank you.

- Dec 14th 2013, 09:09 AMjohngRe: Confirmation
Hi,

Unfortunately I have to say that practically nothing of what you say is correct. In particular, your negation of a sequence a_{n}being a Cauchy sequence is wrong. A sequence is not Cauchy if and only if

$\displaystyle \exists\,\epsilon>0\,\,\forall N\,\exists\, n,m \text{ with }n\geq N,m\geq N\text{ such that }|a_n-a_m|\geq\epsilon$

The problem is "standard"; it is fundamental in proving a "fixed point" theorem. Here is a reference to this fixed point theorem which contains essentially a proof of your problem -- Banach fixed-point theorem - Wikipedia, the free encyclopedia. You want to look at Banach's original proof. - Dec 14th 2013, 09:58 AMdavidciprutRe: Confirmation
Yes, I suspected so... Thank you