On 25 Jun., 20:39, "Mike Terry" <news.dead.person.sto...@darjeeling.plus.com> wrote: > "WM" <mueck...@rz.fh-augsburg.de> wrote in message > > news:firstname.lastname@example.org... > > > > > > > On 24 Jun., 21:26, "Mike Terry" > > <news.dead.person.sto...@darjeeling.plus.com> wrote: > > > There is a starting list L0 and many following lists. During > > construction step n+1 the list is > > > An > > ... > > L0 > > > and has an antidiagonal. > > > The antidiagonals of all these lists are countable but canot be > > written in form of a list (it does not matter if in a separate list or > > in a list with spaces or else), because, if written in form of some > > list, they would yield an antidiagonal that was not in the list. > > OK finally I am certain of what you are saying. > > The "antidiagonals of all these lists" is A0, A1, A2, A3, ... > > Now let me see how I might construct a list which covers all those > anti-diagonals. OK, I've thought of one! My list is: > > L = (A0, A1, A2, A3, ...) > > OK, I've done what you said couldn't be done. Let's look at why you thought > it couldn't be done - perhaps there's a mistake there?
Please let me know: Does the list conssisting of A0, A1, A2, A3, ... contain its antidiagonal or 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.
> > > 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.