On 27 Jan., 14:12, William Hughes <wpihug...@gmail.com> wrote: > On Jan 27, 10:40 am, WM <mueck...@rz.fh-augsburg.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. The latter, however, is claimed to follow.