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Re: Matheology § 201
Posted:
Jan 27, 2013 8:33 AM
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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.
Regards, WM
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