In article <3ef6da97-a35e-445a-9d62-b4df42474711@c10g2000yqi.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> Please let me know: Does the list conssisting of A0, A1, A2, A3, ... > contain its antidiagonal or not?
Not!
> > > > You said that L (as I've defined) has an antidiagonal that's not in the > > list! > > > > I agree that L has an antidiagonal that's not in L. That's normal for > > antidiagonals, but I don't see why you think that's a problem. > > > > IOW we've finally got to the point: > > > > - WM has constructed a countable set of antidiagonals A0, A1, A2, A3... > > > > Define L = the list (A0, A1, A2, A3,...) > > > > - WM claims that AntiDiag (L) is not in L, therefore L does not exist. > > > > - MT points out that L does exist and agrees AntiDiag(L) is not in L, but > > points out this is not a problem. (AntiDiags are never in their input > > lists, so why would anyone think it would be a problem?) > > That is not a problem. It shows however, that there are countable sets > that cannot be listed.
How does it do that? WHICH countable set does WM claim cannot be listed?
By designating a set as countable one guarantees it to be listable, at least for standard definitions of countable and listable.
I have several times asked WM for the distinction that he claims exists between countable and listable, but he has yet to explain that difference to anyone's satisfaction but his own. > > > > > > Hence > > > all antidiagonals of this process, though countable, cannot be written > > > in a list. > > > > Of course they can - you've not shown any problem yet. > > > > Why do you think Antidiag(L) not being in L means that L doesn't exist? > > I do not think so. I said, that there are countable sets that cannot > be listed. One is the set of all antidiagonals of my process. So > countability and listability are not the same.
The claim that the set of all antidiagonals to WM's process cannot be listed has been disproved by constructing a rule for listing that set.
