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

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 William Hughes Posts: 2,330 Registered: 12/7/10
Re: Matheology § 201
Posted: Jan 27, 2013 11:49 AM

On Jan 27, 2:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 27 Jan., 14:12, William Hughes <wpihug...@gmail.com> wrote:
>
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> > 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,
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> >   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