On 22 Jun., 18:27, "Mike Terry" <news.dead.person.sto...@darjeeling.plus.com> wrote: > "WM" <mueck...@rz.fh-augsburg.de> wrote in message > > news:email@example.com... > > > On 22 Jun., 11:49, Sylvia Else <syl...@not.here.invalid> wrote: > > > > The antidiagonal of the list of (A0, A1, A2,...) would only belong to > > > the set if it is also the antidiagnoal of some Ln, which you haven't > > > proved to be the case. > > > Ah, noew I understand. You want to make us believe that there is a > > limiting list but no limiting antidiagonal. > > > The list containing (L0, A0, A1, A2,...) would only then be a list Ln, > > if its antidiagonal is the antidiagonal of some Ln. > > L0 is not a number. It's a list, and so is not eligible for belonging to a > list of numbers. (I.e. this response makes no sense.) > > ----------------- > > So this is where I believe this sub-thread has got to as of Tue 16:00 UTC: > (to stop us going round and around) > > WM has defined a sequence of lists (L0, L1, ...) with corresponding > antidiags (A0, A1, ...). There is a claim that "the set of antidiagonals" > appears to be uncountable, but it was not clear which set this was. > > WM seemed to suggest he meant the set (A0, A1, ...).
No, I added the A's to a list. > > I pointed out this was obviously countable. > > WM agreed but said it can't be written as a list, since it's antidiag is in > the list. > > Sylvia pointed out why this is obviously wrong.
No, she misunderstood. > > WM has now suggested an alternative list (L0, A0, A1,...) but that is not a > valid list of numbers.
I have, from the beginning, used the following list
An ... A2 A1 A0 L0
where L0 is thelist of all rationals.
This list Ln contains a countable set of numbers but the set of its diagonals is not listable, because An is not in the list. > > It is true none the less that the image of L0 is countable, and if we append > all the A0, A1,... it is still countable, so the combined set IS listable. > Suppose LW lists this new set. Of course LW has a NEW antidiagonal which is > not in the list LW, so this isn't going anywhere.
All possiblke diagonals of this set of lists Ln belong to a coutable set, but there is no list of all of them.
It is the same with all Cantor-list. All diagonals of all Cantor-lists belong to a countable set.