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.