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Topic: § 534 Finis
Replies: 6   Last Post: Aug 18, 2014 2:05 AM

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mueckenh@rz.fh-augsburg.de

Posts: 15,366
Registered: 1/29/05
Re: § 534 Finis
Posted: Aug 16, 2014 4:38 PM
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On Saturday, 16 August 2014 21:49:10 UTC+2, Ben Bacarisse wrote:
> mueckenh@rz.fh-augsburg.de writes:
>
>
>

> > On Friday, 15 August 2014 22:32:19 UTC+2, Ben Bacarisse wrote:
>
> >
>
> >
>
> >> > What do you understand by my "misunderstanding"?
>
> >>
>
> >> Exactly what you said: that the sequence of cardinalities should have
>
> >> limit 0 if set theory was right.
>
> >
>
> > In fact, if the set limit was the set at omega.
>

> You'd need to define the WMglish term "the set at omega". I explained
> how set sequence limits can be defined in the little paper I wrote and
> there is no "set at omega" involved.


You mean that paper that has been considered nonsense by everybody who read it?

> You are free to reject these
> limits, or to label them with any WMglish adjective you like, but you
> can't choose what set theory says about it's own definitions.
>

Set theory names the final set of all naturals omega.
>
>

> >> Set theory says that the limit of
> >> cardinalities (we are talking about s_n here, yes?) is exactly what you
> >> expect it to be: oo

>
> >
>
> > What are the infinitely many elements that the cardinality measures?
>
> The limit does not measure anything, because there is no "final set" for
> it to measure. That is the core of you misunderstanding.


It is also Cantor's misunderstanding. The set of all algebraics is a final set because every non-final set contains only a finite number of algebraics and does not allow for Cantor's "proof" of transcendentals.

Didn't you confess to believe in that "proof"?

Regards, WM



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