In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> Am Dienstag, 10. Dezember 2013 14:01:30 UTC+1 schrieb wpih...@gmail.com: >
> > Then you know that for a constructivist there is no list of > > all real numbers.
For a constuctivist there is also no complete list of all rational numbers.
> Here we need a list of all rational numbers only.
Which, other than for constructivists is easy enough.
< This list can be > diagonalized. The first few digits of the antidiagonal cannot prove that the > antidiagonal differs from all rational numbers of the list.
But a general rule, applied equally to all digit positions, can.
> Nobody has ever > seen the following infintely many rationals. We can only prove mathematically > that they are there
So far so good.
> and infinitey many of them are identical with the > antidiagonal for all digits
Actually none of them are identical with CANTOR's antidiagonal for ALL digits. HIS antidiagonal differs from each of them in at least one digit, and in such a way as to guarantee its value is different from that of that rational.
> such that it is impossible to distinguish the > antidiagonal from all of them.
I do not know how WM is constructing HIS antidiagonals, but as Cantor (or one of his students) constructed them, they necessarily differed from each number in the list from which they were constructed. And still do. --