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Topic: fom - 01 - preface
Replies: 3   Last Post: Dec 13, 2012 4:12 AM

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Alan Smaill

Posts: 1,103
Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 12, 2012 2:33 PM
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WM <> writes:

> On 12 Dez., 18:51, Alan Smaill <> 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

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