In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 4 Mai, 14:01, Dan <dan.ms.ch...@gmail.com> wrote: > > On May 4, 12:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 4 Mai, 10:21, Dan <dan.ms.ch...@gmail.com> wrote: > > > > > > > Finite expressions like 1/9 or "0.111111....." cannot occur in the > > > > > course of a Cantor-argument. > > > > > > It's a referent to an infinite expression. > > > > > Of course, but Cantor's anti-diagonals are no referents but infinte > > > expressions. > > > > > > > 0.1 > > > > > 0.11 > > > > > 0.111 > > > > > ... > > > > > > Your list is as finite as "0.111111 ..." . > > > > > That what I have written is finite. It stands for an infinite list. > > > > If your finite writing > > > > 0.1 > > 0.11 > > 0.111 > > ... > > > > stands for an infinite list > > then my finite digit enumeration > > 0.11111 ..... > > stands for infinite digits . Thus disproving your list . > > How would you do that???
The way he just did! > > Either you have digits 1 at finite positions only. Then your number is > in the list, since all finite positions are covered. (You cannot find > that line.
Thus WM is saying that he can have a list of infinitely many rows but still prevent anyone else from having a list of infinitely many columns.
Only in Wolkenmuekenheim!
> > Or you have digits at larger than all finite positions.
Not needed unless you have need lines at more than all finite positions. > > > > Either they're both relevant to Cantor's argument, or they're both > > irrelevant .
Some people, like WM, may claim that the set of real numbers is a countable set.
In order to establish any such claim, those, like WM, who claim it must show that one can have a complete list of all real numbers which includes absolutely every real number, i.e. a surjective mapping from |N to |R, as the existence of such a mapping is the sine qua non of the very definition of countability. Which fact WM carefully ignores.
But the Cantor diaganal argument has shown that any claim to be able to list ALL real numbers necessarily fails to do so.
Thus the definition of countability for the set |R cannot ever be validated.
Thus the set |R cannot be called countable. At least not truthfully. --