On 24 Jun., 02:39, Sylvia Else <syl...@not.here.invalid> wrote: > On 23/06/2010 8:44 PM, WM wrote: > > > > > > > On 23 Jun., 06:47, Sylvia Else<syl...@not.here.invalid> wrote: > > >> Rather than argue that VMs proposition fails on that point, I wanted to > >> address the flaw, in order to find a more substantial objection. > > > My initials ar WM. > > > There is no flaw in the argument: Your bijection either contains all > > constructed antidiagonals. Then a list contains also its antidiagonal, > > because every list has an antidiagonal and your bijection (that is > > only a permutation of my list) contains all lines and antidiagonals. > > I.e., there is no missing antidiagonal of a "limit" list outside of > > the bijection. > > > Or there is a last diagonal of the limit list that does not belong to > > your bijection (and to my list). Then there is a countable set (the > > set that includes this last diagonal) that is not listable. > > > Think over that only a little bit. It is not difficult to understand. > > > Regrads, WM > > Thing is, I just cannot see that you've constructed a countable set that > should contain its own anti-diagonal when expressed as a list.
When it does not contain it, then the antidiagonal is not listed. That is all.
> All > you've done is construct a countable set of countable sets, each of > which contains the anti-diagonals of its predecessors, but none of which > by construction can be expected to contain its own anti-diagonal.
That is why I did it. The set of elements of L0 and antidiagonals A0, A1, ... is countable, but cannot be listed. > > You've then claimed, but without any kind of formal argument, that if > you take this to the limit,
Why should there be a limit? Why should I agrre to take this to a limit? There is no limit in n. Every one is followed by another one.
> the result is a countable set that should > contain its own anti-diagonal when expressed as a list.
Then Cantor's argument would fail. There are no other escapes: Either there is some list that contains its antidiagonal or there is no list that contains it.