On 20 Apr., 19:06, fom <fomJ...@nyms.net> wrote: > On 4/20/2013 11:22 AM, WM wrote: > > > > > > > On 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. > > No.
I withdraw my assertion. Maybe you cannot.
Mathematicians can. Dedekind was a mathematician. Dedekind could. Try to learn, for instance here: Richard Dedekind: Was sind und was sollen die Zahlen? 1887.