abundance of irrationals!)

"Randy Poe" <poespam-trap@xxxxxxxxx> wrote in message news:<1113846213.793230.306610@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>...
> Randy Poe wrote:
> > W. Mueckenheim wrote:
> > > Please repeat your proof
> > > for the infinite Sum 1/2^k = 1, and you will see where you fail.
> >
> > The definition of this infinite sum is a sequence, and
> > you said "sequences cause no problems".
>
> Sigh. The definition of this infinite sum is the
> LIMIT of a sequence, as I stated correctly here:
>
> > By definition, S is the limit of the sequence S_1, S_2,
> > ... where S_n = sum(k=1,n) 1/2^k.

But the limit of the sequence is not a member of the sequence (in
general). Hence Cantor's diagonal is not the limit. Compare the
following:
Write 1/n in the nth line of the list . Does 0 appear in a line?

Regards, WM
.

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