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Re: Matheology § 191
Posted:
Jan 13, 2013 4:33 PM
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On 13 Jan., 21:19, Virgil <vir...@ligriv.com> wrote:
> > A listing of all finite initial segments of all possible tails is
> > possible.
> > Cantor's diagonal argument leads to an anti-diagonal that differs from
> > every finite initial segment by a finite initial segment which is a
> > self-contradiction since all possible finite initial segments that
> > possibly could differ are already there.
>
> Any non-finite sequence, such as an anti-diagonal, NECESSARILY differs
> from every finite sequence
at a finite place, i.e., within a finite initial segment of the anti-
diagonal. (Elsewhere it is impossible to fix a digit which could
differ.) Therefore, if the list contains all possible finite initial
segments, then the anti-diagonal necessarily differs and necessarily
cannot differ from all entries of the list.
How long have you needed to understand the former when you were young?
Have you meanwhile grown too senile to understand the latter, which is
as easy to comprehend?
Regards, WM
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