# Math Help - Confirmation

1. ## Confirmation

Hi I need confirmation, Thank you.

2. ## Re: Confirmation

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

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

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.

3. ## Re: Confirmation

Yes, I suspected so... Thank you