Virgil
Posts:
9,012
Registered:
1/6/11


Re: Matheology S 201
Posted:
Jan 27, 2013 3:22 PM


In article <a4ae5a0011ff485ba8ff473ee82b6ff1@v7g2000yqv.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 27 Jan., 17:56, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > William Hughes <wpihug...@gmail.com> writes: > > > 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. > > > > Frankly, it seems to me that induction is utterly unnecessary. > > > > Once we define the antidiagonal, it is a triviality to show that it > > differs from each line of L. > > > > A minor point, perhaps. > > It the list is complete with respect to all terminating decimals, what > is possible, then the antidiagonal cannot differ from all lines at > finite places. WM may be able to command like that what is allowable inside Wolkenmuekenheim, but not outside of it, and most math is clearly outside of it. 

