In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 20 Apr., 17:15, dullr...@sprynet.com wrote: > > On Sat, 20 Apr 2013 01:16:36 -0700 (PDT), WM > > > > <mueck...@rz.fh-augsburg.de> 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. > > > > Yes... > > > > >U s_n = |N > > >forall n exists i : n e s_i. > > > > >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). > > > > No, that's backwards. n <= i if and only if n is in s_i. > > You are right. The correct and better readable version (from which > this has been copied with some errors) is in > http://www.hs-augsburg.de/~mueckenh/KB/Matheology.pdf > > > > > > > > >There is no term s_n of S that contains all natural numbers. > > > > Obviously not. > > > > So what? > > Small wonder, since nowhere "all" n can be found.
Perhaps nowhere in Wolkenmuekenheim, but then Wolkenmuekenheim is such a small and excessively cramped space that there is a lot of mathematics that doesn't fit in it.
> Why then do you think there would be > infinitely many natural numbers?
Because for each natural there is also a successor natural, a sequence without end. --