In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
Thus in WMytheology one must have the existence of non-existing objects.
I prefer infinities to WM's need for having what one does not have. > > > > 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.
Which is not a relevant answer.
Can WM provide an definition for natural numberss which doe not state, or at least imply, that every natural must have a successor natural? > > > > > 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. > >
> > 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.
So what? There are lot of things in mathematics one cannot do, but that should not keep us from doing what we can do, the way you would limit us.
WM has frequently claimed that his mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping.
In order to show that such a mapping is a linear mapping, WM must first show that the set of all binary sequences is a vector space and that the set of paths of a CIBT is also a vector space, which he has not done and apparently cannot do, and then show that his mapping satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of the field of scalars and x and y and f(x) and f(y) are arbitrary members of suitable linear spaces.
While this is possible, and fairly trivial for a competent mathematician to do, WM has not yet been able to do it.