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Topic: fom - 01 - preface
Replies: 18   Last Post: Dec 12, 2012 3:34 PM

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mueckenh@rz.fh-augsburg.de

Posts: 15,470
Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 12, 2012 1:54 AM
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On 12 Dez., 03:21, fom <fomJ...@nyms.net> wrote:
> On 12/11/2012 12:55 AM, WM wrote:
>

> > On 10 Dez., 21:03, fom <fomJ...@nyms.net> wrote:
> >> On 12/10/2012 11:57 AM, WM wrote:
>
> <snip>
>
>
>
>
>
>
>

> >> Yes. He did. But, Cantor's notion of a real
> >> number was clearly found in the completion of a
> >> Cauchy space.

>
> > That is completely irrelevant for the result.
>
> >>   He found that more appealing
> >> than Dedekind cuts.  This is evident since
> >> his topological result of nested non-empty
> >> closed sets in a complete space is closely
> >> related.

>
> >> There are ordinal numbers in set theory given
> >> the names of natural numbers.

>
> > Only those which are finite.
>
> >> Find a different criticism of Alan's remarks
> >> if you must.  This one is incorrect.

>
> > So you disagree that 2 is a real number?
>
> Since you like quoting the Grundlagen, try
> transcribing long detailed passages from
> section 9


I have written read an written everything Cantor wrote.

> where Cantor rejects definitions
> that conflate logical priority as you have
> been doing.


I have not been doing so. At that time there was no difference between
reals, integers and cardinals (because Cantor did not suspect that
there would apperar a contradiction). He just had switched from oo to
omega. No alpphs in sight.
>
> That is where he calls his construction
>
> "... a fundamental sequence and correlate
> it with a number b, TO BE DEFINED THROUGH
> IT,..."
>


And those numbers are multiplied by real numbers.

[text unrelated to the topic deleted]
>
> So, this time let me suggest
> that you open a new top-level
> post openly apologizing to Alan.


All you have said does not change Cantor's interpretation. Have you
really overlooked his: "da doch auf diese Weise eine bestimmte
Erweiterung des reellen Zahlengebietes in das Unendlichgroße erreicht
ist" ? Or did you want to cheat only?

>
> That is what civil people do when
> they are wrong.-


Then you should excuse yourself to me and to Cantort for completely
misinterpreting Cantor here.

Regards, WM



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