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???
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. This is the same as: For every n there are infinitely many naturals m > n. But you cannot find those which are larger than all n. (Since there are not "all" n.))
Or you have digits at larger than all finite positions. Then you cannot replace them and cannot apply Cantor's argument. > > Either they're both relevant to Cantor's argument, or they're both > irrelevant .
Cantor's argument is a single-eyed look into the infinite. Forall n : d_n =/= a_nn is considered important. Forall n : (d_n) is in the list, is not considered important.