Date: Mar 16, 2013 5:37 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 16 Mrz., 21:19, Virgil <vir...@ligriv.com> wrote:

> > In potential infinity there is no necessary line except the last one.

> > We know that with certainty from induction. Every found and fixed line

> > n cannot be necessary, because the next line contains it.

>

> AS soon as something is identifies as a natural or a FIS of the set of

> naturals, it has a successor. It cannot be either a natural nor a FIS of

> the naturals without a successor. at least by any standard definition of

> naturals.

As soon as a second becomes presence, it has a successor. It cannot be

presence. Nevertheless presence exists.

>

> Can WM provide an definition for natural numberss which doe not state,

> or at least imply, that every natural must have a successor natural?

Numbers are creations of the mind. Without minds there are no numbers.

>

> > Everything that is in the list

> > 1

> > 1, 2

> > 1, 2, 3

> > ...

> > 1, 2, 3, ..., n

> > is in the last line. Alas as soon as you try to fix it, it is no

> > longer the last line.

>

> Thus it is unfixable that where there is a last line there are not all

> lines nor all naturals.

>

>

>

> > Think of the time. What is "now"? As soon as you try to fix it, it is

> > past. In time you can predict the development of clocks. In lists

> > there is no such smooth, predictable evolution. Will the next line

> > added to above list be n+1, or n^2 or n^n^n^n (all those of course

> > also including n+1 and its followers? There are no limits. But as soon

> > as we look onto the last line, we get the idea of another one and that

> > will add one or many lines to the list.

>

> So that the process is endless.

>

> Mathematics outside of Wolkenmuekenheim deals successfully with endless

> processes all the time,

but you are not able to write aleph_0 digits of a real numbers like

1/9. You can only use finite definitions to determine the limit. That

is the successful dealing of mathematics with infinity. The belief,

however, that "there are" aleph_0 digits, does not belong to

mathematics.

Regards, WM