Date: Jan 15, 2013 2:10 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: WMatheology § 191

On 15 Jan., 19:45, Virgil <vir...@ligriv.com> wrote:

> > That does not help. It can only differ at finite places.
>
> It takes infinitely many finite "places" to make an infinite sequence.


That does not help you. There are infinitely many finite initial
sequences such that no finite combination of nodes or digits is
missing.

> And it is quite legitimate to speak of some property as belonging to
> "ALL" of those "places" outside of WMytheology, even though the set of
> such "places" must be an infinite set.


The the following sequence must have all natural numbers as negative
exponents:

1) 10^-1
2) 10^-1 + 10^-2
3) 10^-1 + 10^-2 + 10^-3
...
oo) 10^-1 + 10^-2 + 10^-3 + ... (not containig 10^-oo)

And they all must be in one line. But that line does not exist. There
exists only the limit 1/9. But 1/9 is not a term of this sequence. It
differs from the sequence by having all natural numbers as negative
exponents.

Alas, how can there be all finite terms of the sequence, enumerated by
all finite natural numbers, whereas all natural numbers as exponents
already are beyond the finite terms?

Regards, WM