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Topic: § 534 Finis
Replies: 30   Last Post: Feb 22, 2015 8:14 AM

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: § 534 Finis
Posted: Aug 7, 2014 12:17 PM
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On Thursday, 7 August 2014 17:40:44 UTC+2, Zeit Geist wrote:
>
> > I think the following: For all natural numbers I have shown that uncounted rationals remain.
>
> All Natural Numbers are Finite, too.
>
> Is N Finite?


If infinity can be finished, then N is ""all natural numbers. I have assumed that and have shown that then rationals remain uncounted. But since it is impossible to identify remaining rationals, the original assumption has been contradicted. (It was the only assumption used in my proof that has not been well established as reliable from hundreds of years of mathematics.) Therefore finished infinity has been contradicted. "All natural numbers" is a meaningless notion. So we must say: N contains every natural number. Since there is not a largest one, N is without end, we call it endless or infinite or unfinished.
>
> Using the Same Step in your False Argument can Show it is.


No, it is not. But try to show it.


> > Therefore all natural numbers cannot count all rational numbers.
>
> Therefore All Natural Numbers com Not count All the Natural Numbers.


Correct, since there are not "all natural numbers".

Regards, WM



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