
Re: Matheology § 201
Posted:
Jan 27, 2013 11:49 AM


On Jan 27, 2:33 pm, WM <mueck...@rz.fhaugsburg.de> wrote: > On 27 Jan., 14:12, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > > > > > On Jan 27, 10:40 am, WM <mueck...@rz.fhaugsburg.de> wrote: > > <snip> > > > <... N contains more than all (finite initial segments) > > > Piffle. N does not contain more that all FISONS > > nor has anyone claimed this. > > > the correct statement is > > > For every initial seqment f, there is an element of N, n(f) > > such that n(f) is not in f. (note that n(f) may change if you > > change > > f) > > > However, > > > for ever n(f) there is an initial segment g > > such that g contains n(f) > > Of course. But these all are relative definitions. As I said, it is > impossible to define infinity absolutely. Same is valid for Cantor's > diagonal: For every line n, there is an initial segment of the > diagonal that differs from the first n lines. But that does not imply > that there is a diagonal that differs from all lines.
It does imply that there is a diagonal that differs from each line. We start by noting that if a list L has a finite definition, so does the antidiagonal of L, call it l. By induction we show that l differs from each line of L.
The latter, > however, is claimed to follow. > > Regards, WM

