Re: abundance of irrationals!)

Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx> wrote in message news:<ITSnetNOTcom#virgil-9BE167.17030809042005@xxxxxxxxxxxxxxxxxxxxxxxx>...

> >
> > 1/2^n is a typical term of the sequence. No term of the sequence "over
> > all n e N" is equal to the limit.
> > Why should the above sum over all k e N be equal to the limit?
>
> Because for every positive real epsilon, there is a positive integer m
> such that whenever n >= m then |1 - SUM_{1<=k=<n, 1/2^2| < epsilon.

Whenever n > m means, it must be calculaed for ALL n > m. But a sum
over all n > m is an infinite sum. This ust be calculaed in order to
prove that a limit exists. I.e., it must be possible to calculate it
in advance.

Regards, WM
.

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