In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 26 Jun., 00:32, "Mike Terry" > > > > Please let me know: Does the list consisting of A0, A1, A2, A3, ... > > > contain its antidiagonal or not? > > > > No, of course not. > > The set of all these antidiagonals A0, A1, A2, A3, ... constructed > according to my construction process and including the absent one is a > countable set. > > > > > > > That is not a problem. It shows however, that there are countable sets > > > that cannot be listed. > > > > How exactly does it show that there are countable sets that cannot be > > listed? > > > See the one above: The results of my construction process. > > > > > OK, but you've still not given any explanation why you think the > > antidiagonals of your process cannot be listed! (I'm genuinely baffled.) > > You said so yourself, few lines above.
Saying something does not make it true. WM, for example, often says things which are not true.
Since listable and countable are in all respects identical (logically equivalent properties), there cannot be any set provably countable and provably not listable.