Date: Dec 12, 2012 2:33 PM
Author: Alan Smaill
Subject: Re: fom - 01 - preface

WM <mueckenh@rz.fh-augsburg.de> writes:

> On 12 Dez., 18:51, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
>>
>> A bad translation; it's not the domain that is real, but the numbers:
>
> You agree that the numbers are real? 

I said (and you snipped):

better is "a definite extension of the region of real numbers into the
infinitely large".

>But you do not agree that these
> numbers are real numbers? Remarkable.

You are making no sense.

>>    "The first number-class (I) is the set of finite integers
>>     1,2,3, ...,nu,...,
>
> And you have already forgotten that finite integers are real numbers?

And you have forgotten that you claim Cantor uses multiplication
on reals which are not also cardinals.

>> 3.14159...  does not make an appearance anywhere in these number classes.

Does 3.14159... appear in Cantor's number-classes, then?

> Read § 4, first sentence:
> Die erweiterte ganze Zahlenreihe kann, wenn es die Zwecke fordern,
> ohne weiteres zu einer kontinuierlichen Zahlenmenge vervollständigt
> werden, indem man zu jeder ganzen Zahl alle alle reellen Zahlen x, die
> größer als Null und kleiner als Eins sind, hinzufügt.
>
> Obviously these extended numbers are not ordinals or cardinals -
> unless sets can have fractions of elements.


As I said before, and you have deleted:

  "And what does this give?  an ordered set;  but no multiplication
   defined here, of course! "

Still not a single example of Cantor multiplying a transfinite
number with anything other than another ordinal/cardinal.



>
> Regards, WM

-- 
Alan Smaill