Date: Jan 15, 2013 4:29 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: WMatheology § 191
On 15 Jan., 22:12, Virgil <vir...@ligriv.com> wrote:

> In article

> <3e51ac5e-0aa6-4c17-8353-d6db63f3a...@ho8g2000vbb.googlegroups.com>,

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > 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.

>

> But every infinite combination is missing so any infinite combination

> differs from every finite combination.

Not by nodes or digits. And that is what counts in mathematics.

>

>

>

>

>

>

>

> > > 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.

>

> You prove my point that the infinite sequence is different from every

> finite sequence.

>

The infinite sequence is the first that contains all finite n. What

finite n is missing within the finite terms?

>

>

> > 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?

>

> Which terms in your

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

> are "beyond all finite terms"?

oo is beyond all finite numbers. So the limit 1/9 is beyond all finite

terms.

>

> I do not find anything in it that is beyond all finite terms.

The infinite sequence of 1/9 is the first that contains all finite n.

What finite n is missing within the finite terms?

Regards, WM