"WM" <email@example.com> 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?
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?)
> 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?