In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> n 20 Apr., 17:30, fom <fomJ...@nyms.net> wrote: > > On 4/20/2013 3:16 AM, WM wrote: > > > > > Matheology § 255 > > > > > Let S = (1), (1, 2), (1, 2, 3), ... be a sequence of all finite > > > initial sets s_n = (1, 2, 3, ..., n) of natural numbers n. > > > > > Every natural number is in some term of S. > > > U s_n = |N > > > forall n exists i : n e s_i. > > > > > S is constructed by adding s_(i+1) after s_(i). > > > > Notice that WM is claiming that the sequence has > > a recursive definition. > > You can call it also inductive. > > > > Once again he is assuming the axioms which he > > rejects. > > > Not at all. For every n there is m > n. That's obviously correct in > mathematics without any axioms.
Thus there cannot ever be an upper end to the list of naturals, as for every potential "end" WM now admits that there is a larger one. --