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Re: fom  01  preface
Posted:
Dec 12, 2012 12:51 PM


WM <mueckenh@rz.fhaugsburg.de> writes:
> On 12 Dez., 12:07, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote: >> WM <mueck...@rz.fhaugsburg.de> writes: >> > On 11 Dez., 12:54, Shmuel (Seymour J.) Metz >> > <spamt...@library.lspace.org.invalid> wrote: >> >> In <virgil2FC1D7.13530210122...@BIGNEWS.USENETMONSTER.COM>, on >> >> 12/10/2012 >> >> at 01:53 PM, Virgil <vir...@ligriv.com> said: >> >> >> >In order to define the product of a real number times a >> >> >transfinite, the definition must hold for all reals and all >> >> >transfinites. >> >> >> There's a more fundamental problem; she/he/it is conflating cardinals, >> >> > Cantor was a male. So "he" would be appropriate. >> >> And the problem is passed over in silence by WM. > > No, I mentioned the problem that Shmuel cannot even calculate limits > of sipmle sequences.
As I said, you passed over the problem at issue in silence.
> And again I mention the problem that you cannot > read simple texts: > See: Grundlagen einer allgemeinen Mannigfaltigkeitslehre (Leipzig > 1883)] There he writes: "da doch auf diese Weise eine bestimmte > Erweiterung des reellen Zahlengebietes in das Unendlichgroße erreicht > ist" My translation: Since in this manner a definite extension of the > real domain of numbers into the infinitely large has been > accomplished.
A bad translation; it's not the domain that is real, but the numbers: better is "a definite extension of the region of real numbers into the infinitely large".
And what does this give? an ordered set; but no multiplication defined here, of course!
Indeed, when (ordinal) multiplication is introduced (section 3), it is in the context of Cantor's number classes:
"The first numberclass (I) is the set of finite integers 1,2,3, ...,nu,..., which is followed by a second numberclass consisting of certain infinite integers following each other in a determined succession; after defining the second numberclass, the third is reached, then the fourth etc."
(translation George Bingley)
3.14159... does not make an appearance anywhere in these number classes.
> Regards, WM
 Alan Smaill



