> In article <firstname.lastname@example.org>, > WM <email@example.com> 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.
There's no problem in giving an effective function from |N to the rationals. The intuitionist position is that the rationals are therefore countable. (WM's claim to the contrary notwithstanding.)
There *is* a problem giving such a function from |N to the computable reals.
>> 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.