In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 27 Jan., 18:32, William Hughes <wpihug...@gmail.com> wrote: > > On Jan 27, 6:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > <snip> > > > > >..the diagonal > > > cannot differ from all lines > > > (it differs from every line, though). > > > > The fact that the diagonal differs from every line is > > enough to show (induction) that the diagonal is not > > equal to any line in the list. > > No. Induction shows that induction never proves something for *all* > naturals (simply because in PA there are not *all* naturals.
In ZF and real mathematics there is a set of all naturals. --