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)]