On 20 Apr., 23:27, fom <fomJ...@nyms.net> wrote: > On 4/20/2013 11:22 AM, WM wrote: > > > On 20 Apr., 17:30, fom <fomJ...@nyms.net> wrote: > > >> 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. > > Here I have to use the dogmas of matheology though. > > Then prove your statement for the WM-assumed > greatest natural number. > > You see, when WM uses words like "all" and > "every" those words only have meaning with > respect to finite models.
Not at all. It is the result of the unresolved contradiction that no finished infinity exists. But perhaps someone can resolve the problem:
S is constructed by adding s_(i+1) after s_(i). So we have (1) forall n, forall i : (n < i <==> ~(n e s_i)) & (n >= i <==> n e s_i).
There is no term s_n of S that contains all natural numbers. This condition requires (2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.