> 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.