Date: Dec 12, 2012 12:51 PM
Author: Alan Smaill
Subject: Re: fom - 01 - preface
WM <mueckenh@rz.fh-augsburg.de> 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

> 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 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

--

Alan Smaill