In article <firstname.lastname@example.org>, WM <email@example.com> 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. --