On Dec 10, 9:50 am, WM <mueck...@rz.fh-augsburg.de> wrote: > On 9 Dez., 20:50, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Dec 9, 3:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > infinite? This question is answered with a resounding no. It remains > > > as before and as ever in mathematics: > > > > 1) Every FISON is finite. > > > 2) There are never two FISONs that contain more than one of them. > > > 3) There are all naturals in the FISONs that satisfy (1) and (2). > > > True but irrelevant. Even in Wolkenmuekenheim you can have a > > sequence of FISONs without a last fixed element. > > Any such sequence will have the potentially infinite set N > > as the set of natural numbers in its elements. > > In Wolkenmuekenheim, such a sequence will have a "necessary" FISON > > (your definition). > > However, the "necessary" FISON of one sequence may not be > > in another sequence > > Irrelevant.
In Wolkenmuekenheim it is irrelevant that a necessary FISON is not always needed.
> The necessary FISON is always only one. > > But all that is completely irrelevant, as I do not claim that my model > is correct and as I do not base my reasoning upon that basis. >
You do claim that a sequence of FISONs without last FISON does not exist.
> My reasoning shows that, according to mathematics, all natural numbers > fit into one (potentially in-) finite set.
Nope your reasoning shows that the naturals in any sequence of FISONs with a last FISON, fits into one FISON. Your reasoning says nothing about sequences of FISONs without last element.
Of course you live in Wolkenmuekenheim where
All FISONs have a fixed last element. N does not have a fixed last element. N is a FISON.
makes sense. In part, this is because in Wolkenmuekenheim everything, including fixed last elements, can change. Outside of Wolkenmuekenheim, the idea that a set of naturals without last element (whether actually or potentially infinite) could be contained in a set of naturals with last element is nonsense.
