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Re: Matheology § 201
Posted:
Jan 27, 2013 11:49 AM
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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>
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> > <... |N contains more than all (finite initial segments)
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> > Piffle. |N does not contain more that all FISONS
> > nor has anyone claimed this.
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> > the correct statement is
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> > 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
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> > f)
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> > However,
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> > for ever n(f) there is an initial segment g
> > such that g contains n(f)
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> 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.
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> Regards, WM
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