fom
Posts:
1,969
Registered:
12/4/12


Re: fom  01  preface
Posted:
Dec 12, 2012 11:00 AM


On 12/12/2012 12:54 AM, WM wrote: > 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 nonempty >>>> 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.
wrong
the fundamental sequences ARE the real numbers
> > [text unrelated to the topic deleted] >>
Quite wrong.
That was the text that explained how the wellordered set that is referenced in 2*omega is not described as a fundamental sequence.
Cite the sections from which you are quoting. And quote significantly lengthy passages so that the text is in context.

