Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Matheology � 210
Posted:
Feb 6, 2013 4:47 PM
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In article
<9f8f50d6-1200-4213-9e47-e52cca59c051@x15g2000vbj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> Cantor proves: For every line a_n the inequality a_nn =/= d_n implies
> a_n =/= d.
>
> This implies: For *every* line a_n: (a_n1, a_n2, ...., a_nn) is
> *finite*.
but does not imply that a line ending in a_nn is the whole of line n
>
> In words: The proof unavoidably requires that the lines a_n, with no
> exception, are finite up to the crucial point a_nn - and the rest is
> silence.
Meaning that the "rest" of any such line can be anything from empty to
infinitely long
> The rest has *nothing* to do with the proof, and if the rest
> is empty, the proof is not in the least changed.
> No individuation.
> Try to *apply* logic.
WE would like to, but every time we try, WM objects.
Given a finite set of "digits" appearing as elements in those lines, one
can always create a new digit different from all of them and "complete "
each finite line with infinitely many copies of the new digit, thus
reducing the problem to Cantor's original format of all lines being
infinite.
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