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Topic: Matheology § 201
Replies: 32   Last Post: Jan 28, 2013 2:26 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology S 201
Posted: Jan 27, 2013 3:22 PM

In article
WM <mueckenh@rz.fh-augsburg.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.fh-augsburg.de> wrote:
> > >> 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.

> >
> > > 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 anti-diagonal, 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 anti-diagonal 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.
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