In article <email@example.com>, WM <firstname.lastname@example.org> 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.
A Cantor antidiagonal is a rule for creating an infinite sequence of decimal digits just like "Sum_(n in |N) 1.10^n" is such a rule. > > > > > > 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.
Just as the finite description of the Cantor anti-diagonal stands for an infinite sequence of decimal digits defining a real number.
> In order to prove uncountability Cantor's anti-diagonal has to work in > case of infinite lists (without finite definitions) too.
Note that in order for WM to claim that the reals ARE countable, WM must prove that there is a list containing all reals (i.e., a surjection from |N to |R).
But whenever WM, or anyone else, for that matter, ever claims that, Cantor's diagonal argument proves their claim false.
> There it has > to be an infinite sequence of digits.
Not unless there also has to be an infinite sequence of reals containing every single real.
Or does WM claim that |R need be neither countable nor uncountable, but can be something different from either? --