Date: Dec 12, 2012 2:33 PM
Author: Alan Smaill
Subject: Re: fom - 01 - preface
WM <email@example.com> 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
>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