Hello

It is (defines a dot product)

Show that is a cauchy-sequenze

(field) norm:

--------------

I think is okay, but it is

any help would be really apprectiated

Rapha

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- Nov 10th 2008, 08:29 AMRaphacauchy-sequenze
Hello

It is (defines a dot product)

Show that is a cauchy-sequenze

(field) norm:

--------------

I think is okay, but it is

any help would be really apprectiated

Rapha - Nov 10th 2008, 09:34 AMOpalg
Let m<n. We want to show that as , where . But and coincide on the intervals [0,1-(1/m)] and [1,2]. So we need only worry about the integral on the interval from 1-(1/m) to 1. Even on this interval, the integral is a bit messy to evaluate exactly, so I suggest using a little trick.

It's easy to see that if m<n then . Therefore , and the integral that we want to evaluate is less than . That integral is (very!) easy to evaluate, and it gets small as m gets large.