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Topic: fom - 01 - preface
Replies: 3   Last Post: Dec 13, 2012 4:12 AM

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mueckenh@rz.fh-augsburg.de

Posts: 15,737
Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 13, 2012 2:35 AM
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On 12 Dez., 20:33, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

>
> And you have forgotten that you claim Cantor uses multiplication
> on reals which are not also cardinals.


No, that I did not! Here is
my claim:

AS: Aleph_0 is not a length, nor an area, nor a volume.

WM: 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.

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

WM: You are badly informed.

AS: 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?

WM: 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)]

Regards, WM



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