In article <8a924020-947b-43cf-8ca9-d011c05b1b43@s9g2000yqd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 27 Jun., 13:01, "Mike Terry" > <news.dead.person.sto...@darjeeling.plus.com> wrote: > > > > 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!. > > But that is not the question! Please read carefully. The question is > whether there is a countable set that cannot be listed. This set is > given by the original list and all its possible antidiagonals.
That presumes that the set of all its possible "antidiagonals", i.e., nonmembers, is countable, which begs the question.
If one has a particular rule for creating an antidiagonal of a listing and then inserting it in that listing, that all the elements of the original list and all constructed elements can be listed in onew list quite easily, and several such methods have been shown here, which WM has carefully ignored.
> > > > 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)). > > And your (a) and (b) ist obviously irrelevant for the present > discussion. > > > > So you are wrong. > > No. You simply cannot understand the meaning of a process which cannot > end (hence the results of which cannot be put in a complete list) > unless there is a list containing its antidiagonal.
The set of naturals does not end, but can be "listed", so that "not ending" is not a valid objection. Any set which can be recursively defined can obviously be listed, just like the naturals, and the set that WM objects to being listable IS recursively defined.
> But as I have > given the description in clear words, I don't want to repeat it. > Probably it would not support your understanding either.
What is "clear" to WM is often not clear to anyone else, and what is clear to everyone else is often not clear to WM.
WM's "mathematics" and the mathematics of the rest of the world have limited overlap. > > You may google under "supertask" to better inform you.
According to Zeno, and WM, moving from point A to point B would be one of those impossible supertasks. But those of us not aware of its impossibility in their worlds do it anyway.
