In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Cantor proves: For every line a_n the inequality a_nn =/= d_n implies > a_n =/= d. > > This implies: For *every* line a_n: (a_n1, a_n2, ...., a_nn) is > *finite*. but does not imply that a line ending in a_nn is the whole of line n > > In words: The proof unavoidably requires that the lines a_n, with no > exception, are finite up to the crucial point a_nn - and the rest is > silence.
Meaning that the "rest" of any such line can be anything from empty to infinitely long
> The rest has *nothing* to do with the proof, and if the rest > is empty, the proof is not in the least changed. > No individuation. > Try to *apply* logic.
WE would like to, but every time we try, WM objects.
Given a finite set of "digits" appearing as elements in those lines, one can always create a new digit different from all of them and "complete " each finite line with infinitely many copies of the new digit, thus reducing the problem to Cantor's original format of all lines being infinite. --