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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: 15,281
Registered: 1/29/05
Re: ? 533 Proof
Posted: Aug 1, 2014 4:44 PM
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On Friday, 1 August 2014 19:34:39 UTC+2, Martin Shobe wrote:


> > The number of unit intervals, each one containing infinitely many rationals without index =< n, increases infinitely, i.e., beyond any upper bound.

>
> This is not evidence that the rationals cannot be enumerated by the
> naturals.


It is, because only natural numbers can index. But for every natural numbe I can show that it is not sufficient. Therefore you must believe in something unmathematical. To beleiev this requires a cerebral defect that most mathematicians do not have acquired.
>
>
>

> > Of course a matheologian will brush this aside by the standard blether "cardinals are not continuous".
>
>
>
> I have no idea what a matheolgian would do, but a mathematician wouldn't
> brush it aside that way. They would point out that "the rationals cannot
> be enumerated by the naturals" doesn't follow from "The number of unit
> intervals, each one containing infinitely many rationals without index
> =< n, increases infinitely".


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

> > But everybody with a critical intellect will ask *why* he should believe this.
>
>
>
> And everybody with an ounce of mathematical ability will notice that
> it's because we can prove it.


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.
>
> Back to the Ad Hominems again.
>

Unfortunately a thought is not independent of the human who thinks it. If a proof shows that every natural fails but you can "prove" the contrary, based on the false assumption that infinite sets can be exhausted like finite sets, then only a defect can prevent you to recognize this obvious error.

Regards, WM



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