In article <585af7cf-32f4-4727-9136-620fd3cfd83f@c13g2000vbh.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 9 Dez., 18:47, William Hughes <wpihug...@gmail.com> wrote: > > On Dec 9, 1:23 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 9 Dez., 17:15, William Hughes <wpihug...@gmail.com> wrote: > > > > > > Let T be a non-empty sequence of FISONs without a last fixed element. > > > > > F_1 = {1} > > > F_2 = {1, 2} > > > ... > > > F(t) = F_n = {1, 2, ..., n} > > > > > The last element is not fixed but is a function of a variable about we > > > don't yet know much. It may depend on time, ressources and the > > > distribution of them and on much more. But it is not necessary to > > > introduce reality and psychology into mathematics, as long as we > > > accept potential infinity sinply as inexhaustibility. > > > > > > The set, M, of naturals contained in the elements of T is a > > > > potentially > > > > infinite set. > > > > > The number of naturals in M(t) is the number of numbers in the > > > temporarily last FISON F(t). It is equal to the number of FISONs in > > > T(t). > > > > > > For every natural n, we can find a FISON, F(n), so that n is in F(n). > > > > > And for every function of that natural like 10^10^n. > > > > > > Every natural is in M > > > > > > M is the potentially infinite set N. > > > > > M(t) is a finite set with a last element m. Therefore the FISON F_m > > > which contains m is the only necessary FISON - until w takes the place > > > of m, then F_m is no longer necessary but F_w is the necessary FISON. > > > > Oh, of course, in Wolkenmuekenheim everything changes. > > However, unless you take great liberties with the meaning > > of "necessary" there is still no "necessary" FISON. > > > > Let G be the necessary FISON in any or all of its forms. > > > > Then assume that U is a sequence of FISONs without fixed last > > element (so that the set V, or naturals in the elements of U > > is the potentially infinite set N) > > > > G need not be an element of U. > > > > So G is "necessary" but not needed. > > Does this joke help you to make black white or to make finite > 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. 2') For every 2 fisons, both always contain more that one of them.
Note that these two statements, 2 and 2', are equally true.
> 3) There are all naturals in the FISONs that satisfy (1) and (2)
Which includes all infinitely many fisons!
> It would be nice if you could return to mathematical principles.
It wold be nice if you found even a few of them for a first time. --
