In article <382a8f19-157c-4c0a-9ed2-b9c295ce0dd8@5g2000yqz.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> 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?
No list contains its antidiagonal, nevertheless, any list together with its antidiagonal can be listed, and in a large variety of ways. > > You said no. Therefore your assertion "which CAN be listed" is plainly > wrong.
Nonsense. > > > > Of course it is not possible to list a list and its antidiagonal.
Whyever not?
Given a list {b0, b1, b2, ...} and its antidiagonal, a, how is the llist {a, b0,. b12, b2, ...} NOT a list of the original list plus 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.
Since any such list has potentially uncountably many "antidiagonals", of course not.
But any list along with up to countably many of its antidiagonals can be collectively listed. > > > > Go on - have one more go, then I'll give up... > > You'd better give up than make contradictory claims.
Good advice. Its a shame its author doesn't follow it himself.
