Date: Mar 16, 2013 5:37 PM
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
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