```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 theinfinitely large".And what does this give?  an ordered set;  but no multiplicationdefined here, of course! Indeed, when (ordinal) multiplication is introduced (section 3), it isin 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
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