Date: Dec 12, 2012 12:51 PM
Author: Alan Smaill
Subject: Re: fom - 01 - preface
WM <email@example.com> writes:
> On 12 Dez., 12:07, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> > On 11 Dez., 12:54, Shmuel (Seymour J.) Metz
>> > <spamt...@library.lspace.org.invalid> wrote:
>> >> In <virgil-2FC1D7.13530210122...@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
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
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 number-class (I) is the set of finite integers
1,2,3, ...,nu,..., which is followed by a second number-class
consisting of certain infinite integers following each other
in a determined succession; after defining the second number-class,
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