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Topic: � 534 Finis
Replies: 5   Last Post: Aug 9, 2014 12:21 PM

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 YBM Posts: 846 Registered: 11/27/09
Re: ? 534 Finis
Posted: Aug 9, 2014 12:21 PM

Le 09/08/2014 18:16, mueckenh@rz.fh-augsburg.de a écrit :
> On Saturday, 9 August 2014 15:27:11 UTC+2, YBM wrote:
>
>

>>> Is 0.d_1, d_2, d_3, ... a finite expansion?
>>> Does Cantor's diagonal argument concern a finite list only?
>>> What is the difference between my "forall" and the others?

>>
>> The difference is that Cantor did not use sophistry, fuzzy wording and
>> wasn't dishonest, stupid and stubborn as I am.

>
> Cantor frequently used induction for showing something about infinite sets.

>>
>> Cantor :

>
>> Given s: N->R an enumeration of R
>
> Nonsens. Cantor, original: Über eine elementare Frage der Mannigfaltigkeitslehre. [Jahresbericht der Deutsch. Math. Vereing. Bd. I, S. 75-78 (1890-91).]
>
> Ist E1, E2, ..., E?, ... irgendeine einfach unendliche Reihe von Elementen der Mannigfaltigkeit M
>
> Is ... any infinite sequence ...
>
> Es werde nun eine Reihe b1, b2, ..., bn, ..., so definiert
>
> A sequence is defined.
>
> so sieht man ohne weiteres, daß die Gleichung E0 = En
> für keinen positiven ganzzahligen Wert von n erfüllt sein kann,
>
> for no psitive integer value of n satisfied.
>
> Throughout the whole argument only finite integers. No matheological nonsense.
>

>> neg-Prop : Forall n in N : antidiagonal(s) != s(n)
>>

> Correct. For all n in |N. And not the least little bit more.
>

>> let s: N->Q an enumeration of Q
>
>> Prop : for all n in N:
>>
>> the set Q \ { s(k) : k <= n } is infinite

>
> and growing, growing, dreadfully, terriby growing.
>

>> well, that's true. So what ?
>
> The emperor is naked. So what?
>

>> There is NO WAY without sophistry and without playing with fuzzy
>> wording to conclude that s is not an enumeration of Q.

>
> Ask him to hand you a piece of his clothing.
>
> Regards, WM
>