In article <1fe50c9e-496c-401c-aa55-306e93ae8844@s9g2000yqd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Jun., 13:54, Sylvia Else <syl...@not.here.invalid> wrote: > > On 23/06/2010 8:34 PM, WM wrote: > > > > > > > > > > > > > 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)? > > > > I don't understand why you've recast it back to that form. > > That is a an abbreviation of the construction I proposed. Of course > the "..." stand only for an infinite sequence of well defined digits > at finite places.
Then your definition is flawed in one more way, and totally useless.
One cannot have an antidiagonal of a list in which the elements are not all sequnces of the same type, and here, LO is not of the same type as A0 or A1 or A2 or any An.
> > > You can't > > even form the anti-diagonal of that - what would the first digit of the > > antidiagonal be? > > What would the last digit of a normal Cantor-diagonal?
In order to define a "Cantor antidiagonal' for a set of sequences, S, one must first have a bijection f:N -> S. WM has not made clear that he even has such a bijection, much less what it is like.
> Why should the > first digit be more important than the last one?
Why claim there is a "last one" when infinite sequences of digits don't have any "last ones"?
> An infinite sequence > of digits (that is not converging and not defined by a finite formula, > like Cantor's diagonal sequence) is as undefined when the last digit > is missing as it is when the first digit is missing.
I think WM's first digit is missing! The whole point of an infinite sequence is that there isn't any such thing as a "last"term.
So any demand for one marks the demander as muddled.
