In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 15 Jun., 14:45, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> > wrote:
> > Computing the diagonal number is actually very easy. > > Therefore the diagonal number is a computable real.
Given a list of computable numbers, it is, but one can also have a list containing uncomputable numbers.
> Then Cantor's proof works exclusively on a countable set, namely the > set of computable reals.
All one requires is that for each listed number a different decimal digit position can be computed. So that, for example if the list is such that the nth number can be computed to its nth decimal place, the list need not contain ANY computable numbers at all. > > And it shows that this set is uncountable.
Since any such "antidiagonal" is at least computable from the list, all it shows is that any list of reals is incomplete.
> This result is wrong.
That is what WM claimed years ago, and still has not proved.