In article <80b2050f-d15f-4795-bed8-4ec38a2272fc@z25g2000vbs.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 13 Dez., 20:58, Virgil <vir...@ligriv.com> wrote: > > > > > Every F(n) is finite does imply: There is no infinite FISON. > > > > But does not imply that the number of fisons or the set of all fisons is > > any more finite > > That is without interest. Here we investigate how many natural numbers > can exist within one FISON, and whether more natural numbers than can > exist in any FISON can exist in a set of many or more FISONs. > > > > Given |N, then n -> n+1 is an injection but not a surjection of |N to > > itself, thus |N is by definitin infinite. > > > That is without interest.
It is of interest to everyone but WM, who cannot escape from his Wolkenmuekenheim, for long enough to take interest in reality.
> Here we investigate
You mean here you try to dictate, but as your rulings carry no force, you are not able to dictate.
> how many natural numbers can exist
That is the question that WM keeps trying to avoid, since there can be more of them existing than any since natural number can specify. > > > > > All FISONs that exist belong to a inclusion monotonic sequence does > > > imply: There is, under no circumstances, a set of FISONs that contains > > > more than a single FISON contains. > > > > But it does not imply that the number of fisons is finite > > > That is without interest.
It is of great interest outside Wolkenmuekenheim.
>Here we investigate how many natural numbers > can exist within one FISON
WM may want to limit his own investigations to that, but no one else need be so limited.
> and whether more natural numbers than can > exist in any FISON can exist in a set of many or more FISONs.
MOre natural can, and do, exist in the set of all fisons that exist in any one fison, since it is trivial to prove that there cannot be a last/largest fison. The existence of any on fison proves the existence of its larger successor. > > > and, just as > > above one can prove the set of naturals to be infinite one can prove the > > set of all fison to be equally infinite. > > That is without interest.
It is of considerable interest everywhere outside of Wolkenmuekenheim.
> Here we investigate how many natural numbers > can exist
