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

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 11, 2012 1:55 AM

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

> > On 10 Dez., 18:24, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >> WM <mueck...@rz.fh-augsburg.de> writes:
> >>> On 9 Dez., 23:40, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >>>> WM <mueck...@rz.fh-augsburg.de> writes:
> >>>>> On 8 Dez., 23:37, Virgil <vir...@ligriv.com> wrote:
> >>>>>> Aleph_0 is not a length, nor an area, nor a volume.
>
> >>>>> If it was a whole number or integer, as Cantor insisted, then it could
> >>>>> be used to define a length or an area or a volume etc.

>
> >>>> Cantor defined it as a cardinal number;
> >>>> he did not propose any notion of multiplication of,
> >>>> eg real numbers by transfinite cardinals.

>
> >>> You are badly informed.
>
> >> Then please inform me;
> >> did Cantor consider 3.14159...  to be a cardinal number?
> >> In which of Cantor's number classes does 3.14159... fall?

>
> > First you said something else, namely: "he did not propose any notion
> > of multiplication of, eg real numbers by transfinite cardinals". This
> > claim is wrong because 2, 3, .. are real numbers. Cantor defined
> > 2*omega, 3*omega, ...
> > [Grundlagen einer allgemeinen Mannigfaltigkeitslehre (Leipzig 1883)]

>
> 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?

Regards, WM

Date Subject Author
12/10/12 Alan Smaill
12/10/12 mueckenh@rz.fh-augsburg.de
12/10/12 fom
12/11/12 mueckenh@rz.fh-augsburg.de
12/11/12 Virgil
12/11/12 fom
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/12/12 fom
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/10/12 Virgil
12/11/12 Shmuel (Seymour J.) Metz
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/12/12 Shmuel (Seymour J.) Metz
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil