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