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. However, as you certainly know, the number of all finite words is countable. And the number of all languages interpreting these words is finite (since a language has to be made by someone and to be distributed over sets of participants). All diagonals resulting from those cases belong to a countable set.
In order to prove uncountability Cantor's anti-diagonal has to work in case of infinite lists (without finite definitions) too. There it has to be an infinite sequence of digits. In my finitely referenced example I show that this is impossible.