fom
Posts:
1,702
Registered:
12/4/12
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Re: Matheology § 210
Posted:
Feb 6, 2013 11:10 PM
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On 2/6/2013 12:51 PM, WM wrote:
> On 6 Feb., 19:16, fom <fomJ...@nyms.net> wrote:
>> On 2/6/2013 8:46 AM, WM wrote:
>>
>>
>>
>>
>>
>>> 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.
Before he proves. He asserts the presumption of the presumed
claimant. That presumption involves a one-to-one
correspondence. A one-to-one correspondence is not
a one-to-many correspondence.
>
> This implies: For *every* line a_n: (a_n1, a_n2, ...., a_nn) is
> *finite*.
>
Yes. Cantor identifies a terminating search for each line
in order to make stepwise decisions on what symbol to use
in extending the sequence of symbols that form the counter-example.
> 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.
No. The counter-example only requires a terminating search
for each line. The proof requires a presupposition of
individuated numbers named using a consistent naming algorithm
based on a finite set of sequentially ordered symbols.
> 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.
And with the two words of this sentence, you identify your
complete and total ignorance of...
> Try to *apply* logic.
...what it means to apply logic.
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