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. 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.
Find a different criticism of Alan's remarks if you must. This one is incorrect.