```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 bepresence. 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 like1/9. You can only use finite definitions to determine the limit. Thatis the successful dealing of mathematics with infinity. The belief,however, that "there are" aleph_0 digits, does not belong tomathematics.Regards, WM
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