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? Your remark is incorrect.