
Re: Matheology S 201
Posted:
Jan 27, 2013 12:46 PM


WM <mueckenh@rz.fhaugsburg.de> writes:
> 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.
I wasn't trying to enter a second discussion with you. I just wanted to raise a minor point with William.
I'd prefer to keep to one conversation at a time with you, so that we can focus on a single point of contention.
 Jesse F. Hughes "Disney has now succeeded in preventing anyone from doing to Mickey Mouse what Disney did to Quasimodo."  Randolph Rackovitz, on Eldred vs. Ashcroft

