In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 12 Dez., 00:43, Virgil <vir...@ligriv.com> wrote: > > > > That is potential infinity. There is no set of natural numbers that is > > > larger than every FISON. > > > > While there is no set of natural numbers larger than every SET of > > fisons, there is a set of natural numbers larger than any single fison, > > This is impossible, because all natural numbers belong to a single > FISON by definition of the inclusion monotonic set of FISONs obtained > from the set of exponents of the sequence (a_k) with a_k = 10^-1 + > 10^-2 + ... + 10^-k.
The objects of that definition coincides with the John von Newumann naturals, which collectively form an actually infinite set in ZFC.
I.e., it is a set allowing injection to a proper subset.
For example, the mapping n -> n+1 maps the set of all JvN naturals to a proper subset of the set of all JvN naturals.
Or does WM claim to be able to find some n for which there does not exist any n+1? --