In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> That means that every real that shall be used in mathematics needs a > finite representation over a countable alphabet (even a finite > alphabet - but that does not matter here).
That depends entirely on HOW it is used. In the decimalized form of Cantor's diagonal argument, real numbers of unspecified values can be shown to be listed and for any such listing a real of unspecified but somewhat constrained value can be shown not to be listed in that list. --