On 12 Dez., 03:21, fom <fomJ...@nyms.net> wrote: > On 12/11/2012 12:55 AM, WM wrote: > > > On 10 Dez., 21:03, fom <fomJ...@nyms.net> wrote: > >> On 12/10/2012 11:57 AM, WM wrote: > > <snip> > > > > > > > > >> 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? > > Since you like quoting the Grundlagen, try > transcribing long detailed passages from > section 9
I have written read an written everything Cantor wrote.
> where Cantor rejects definitions > that conflate logical priority as you have > been doing.
I have not been doing so. At that time there was no difference between reals, integers and cardinals (because Cantor did not suspect that there would apperar a contradiction). He just had switched from oo to omega. No alpphs in sight. > > That is where he calls his construction > > "... a fundamental sequence and correlate > it with a number b, TO BE DEFINED THROUGH > IT,..." >
And those numbers are multiplied by real numbers.
[text unrelated to the topic deleted] > > So, this time let me suggest > that you open a new top-level > post openly apologizing to Alan.
All you have said does not change Cantor's interpretation. Have you really overlooked his: "da doch auf diese Weise eine bestimmte Erweiterung des reellen Zahlengebietes in das Unendlichgroße erreicht ist" ? Or did you want to cheat only?
> > That is what civil people do when > they are wrong.-
Then you should excuse yourself to me and to Cantort for completely misinterpreting Cantor here.