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

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: fom - 01 - preface
Posted: Dec 10, 2012 3:53 PM

In article
WM <mueckenh@rz.fh-augsburg.de> 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)]

In order to define the product of a real number times a transfinite, the
definition must hold for all reals and all transfinites.

In order to define the product of a natural and a transfinite the
definition must hold for all naturals and all transfinites.

2 and 3 are also complex numbers and quaternions, so that, according to
WM, Cantor defined both complex times transfinite and quaternion times
transfinite multiplications.
--

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