"WM" <mueckenh@rz.fh-augsburg.de> wrote in message news:382a8f19-157c-4c0a-9ed2-b9c295ce0dd8@5g2000yqz.googlegroups.com... > On 26 Jun., 23:14, "Mike Terry" > <news.dead.person.sto...@darjeeling.plus.com> wrote: > > "WM" <mueck...@rz.fh-augsburg.de> wrote in message > > > > news:511dd6ef-6fe7-4664-bda0-082971c2f8db@z10g2000yqb.googlegroups.com... > > > > > On 26 Jun., 00:32, "Mike Terry" > > > > > > > Please let me know: Does the list consisting of A0, A1, A2, A3, ... > > > > > contain its antidiagonal or not? > > > > > > No, of course not. > > > > > The set of all these antidiagonals A0, A1, A2, A3, ... constructed > > > according to my construction process and including the absent one is a > > > countable set. > > > > Yes, I've agreed that several times. > > > > > > > > > > > That is not a problem. It shows however, that there are countable sets > > > > > that cannot be listed. > > > > > > How exactly does it show that there are countable sets that cannot be > > > > listed? > > > > > See the one above: The results of my construction process. > > > > No. The above shows that you've constructed a countable sequence of numbers > > (A0, A1, A2, A3,...) which CAN be listed, namely consider the list (A0, A1, > > A2, A3,...). > > > > Read carefully! > > In order to do so, I posed the question: Does the list consisting of > A0, A1, A2, A3, ... contain its antidiagonal or not? > > You said no. Therefore your assertion "which CAN be listed" is plainly > wrong.
The fact that a list does not contain its antidiagonal does not mean the list cannot be listed!.
My final word on this:
The set you have constructed: {A0, A1, A2,...} is:
a) countable b) can be listed, e.g. (A0, A1, A2,...) c) of course the list (A0, A1, A2,...) has an antidiagonal Aw, which is not in {A0, A1, A2,...). (This is obviously irrelevent to (a) and (b)).
So you are wrong. (Wrong not in a subtle way, but just in the way of not understanding the basic usage of the mathematical terms involved, like "countable" "list" etc.
Regards, Mike.
> > > > Of course it is not possible to list a list and its antidiagonal. > > > > > > > > > > > > OK, but you've still not given any explanation why you think the > > > > antidiagonals of your process cannot be listed! (I'm genuinely > > baffled.) > > > > > You said so yourself, few lines above. > > > > Rubbish. I have never said anything other than that (A0, A1, A2, ...) is a > > countable sequence of reals that CAN be listed > > but not with all its antidiagonals. > > > > Go on - have one more go, then I'll give up... > > You'd better give up than make contradictory claims. > > Regards, WM
