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Re: Matheology § 210
Posted:
Feb 6, 2013 1:51 PM
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On 6 Feb., 19:16, fom <fomJ...@nyms.net> wrote:
> On 2/6/2013 8:46 AM, WM wrote:
>
>
>
>
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> > On 6 Feb., 02:34, fom <fomJ...@nyms.net> wrote:
> >> On 2/5/2013 11:02 AM, WM wrote:
>
> >>> On 5 Feb., 17:06, fom <fomJ...@nyms.net> wrote:
> >>> This correspondence is as impossible, as I have shown above, as
> >>> finding a set of natural numbers with negative sum.
>
> >> No.
>
> > If you think no, then explain this:
>
> > Have you ever seen a Cantor-list where more than half of the
> > interesting sequences (a_j) of digits a_kj with k < j had infinite
> > length? Have you ever seen a Cantor-list with at least one of the
> > interesting sequences of digits having infinite length? No? Why the
> > heck do you believe that they play the crucial role in Cantor's
> > "proof"?
>
> It is called individuation.
>
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*.
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. 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.
Regards, WM
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