On 23 Jun., 04:18, Sylvia Else <syl...@not.here.invalid> wrote: > On 23/06/2010 11:33 AM, Sylvia Else wrote: > > > > > > > On 23/06/2010 11:03 AM, Virgil wrote: > >> In article > >> <2000e81b-7c5a-41be-b6af-98f96f2fb...@w31g2000yqb.googlegroups.com>, > >> WM<mueck...@rz.fh-augsburg.de> wrote: > > >>> On 22 Jun., 21:34, Virgil<Vir...@home.esc> wrote: > > >>>>>> But (A0, A1, A2, ...) is obviously countable. Above you say it's > >>>>>> "certainly > >>>>>> not countable", but it is. > > >>>>> The set is certainly countable. But it cannot be written as a list > > >>>> But it HAS been written as a list (A0, A1, A2, ...), > > >>> Does this list contain the anti-diagonal of (..., An, ... A2, A1, A0, > >>> L0)? > > >> Since (..., An, ... A2, A1, A0, L0) does not appear to be a list, why > >> should there be any antidiagonal for it? > > > Ach! Let's scrap A0 - it's confusing. > > > If we let L_n be the nth element in the list L0, and An the > > anti-diagonal of the An-1, An-2,...., A1, L_1, L_2, L_3,... > > > then > > > L_1 > > A1 > > L_2 > > A2 > > L_3 > > A3 > > L_4 > > ... > > > is a list. I'm still thinking about that. > > > Sylvia. > > Hmm... > > A1 is the antidiagonal of L1 L2 L3... > > A2 is the antidiagonal of L1 A1 L2 L3... > > A3 is the antidiagonal of L1 A1 L2 A2 L3 L4... > > Each An is thus constructed from a list that is different from the list > into which it is inserted. So the construction does not lead to a list > that should contain its own anti-diagonal, and it doesn't.
Ln =
An ... A2 A1 A0 L0
Does your bijection contain the anti-diagonal of (..., An, ... A2, A1, A0, L0)? If yes, then Cantor's argument fails as a list contains its antidiagonal. Reason: you list in your listing above only the lines of lists. That is so because the antidiagonal of every list Ln belongs to another list L(n+1)).
b) Does it not? Then a list cannot list all anti-diagonals that belong to the countabe set constructed in my argument.
