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Topic: ? 533 Proof
Replies: 46   Last Post: Aug 4, 2014 8:39 PM

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mueckenh@rz.fh-augsburg.de

Posts: 16,037
Registered: 1/29/05
Re: ? 533 Proof
Posted: Aug 2, 2014 5:19 PM
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On Saturday, 2 August 2014 22:54:24 UTC+2, Martin Shobe wrote:

> Less unambiguously, you can show that every finite initial segment of N
> is not sufficient.


And *if there is more in |N* than every finite initial segment, then the limit shows that even this "more" is not sufficient. But who would confess his belief that |N contains more than every finite natural number (tantamount to every finite segment)? He would become ridiculous in mathematics because he cannot answer what this "more" should be.
>

> Therefore you must believe in something unmathematical.
>
> What's unmathematical about thinking that N isn't a finite initial
> segment of N.


You are trying to cheat again and again. |N is not a finite initial segments but all finite initials segments or numbers. What else?
>

> > It follows from the proof that every natural numbers fails. Enough for a mathematician.
>

> Go ahead and prove that "the rationals cannot be enumerated by the
> naturals" follows from "The number of unit intervals, each one
> containing infinitely many rationals without index =< n, increases
> infinitely".


No problem. The fact already that you are trying to cheat would make every objective reader suspicious.
>
>

> > For that "proof" you have to assume that every is tantamount with all. This, however, is a very naive way of thinking that infinite sets can
> be exhausted like finite sets.

>
> It's still proven.
>

It is proven to be very naive.

A proof is a convincing argument. Your argument will not convince anybody without matheological indoctrination when being contrasted with mine.

Regards, WM



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