In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 12 Jan., 23:03, Virgil <vir...@ligriv.com> wrote: > > > > You are invited to "discern" another path from the countable bunch of > > > infinite paths that I used to construct the Binary Tree. > > > > Until you list the ones that you used, there is no way to "discern" > > another, but any list you provide also provides a nonmember. > > Please do that work for me, if you like to have such a list. I told > you already that I appended every definable tail.
Why should I like to have something which does not exist?
If WM wants to claim such a list exists, then HE is reqponsible for proving it, and the only valid proof is to present us with it, or at lest some unambiguous rule for generating it. Neither of which has WM don or can WM do. > > But your idea of listing is not very usefu in this context. Consider > the list of all Cantor-lists that are possible (i.e., definable) and > append all anti-diagonals that are possible (i.e., definable), then > you get a list that cannot be diagonalized because it contains its > anti-diagonal already.
WM must first prove that a "list of all Cantor lists" is possible before using it to prove something else.
And how does one "append" things to a list (the list of all Cantor-lists that are possible) that appears to have no end?
Since we already know that a list of all binary sequences is NOT possible, no one but WM is willing to accept that such a list as he requires can exist without proof that it does exist.
> And if you would try to diagonlize the > countable union of all this countable stuff you must fail, because > this stuff already contains all anti-diagonals of infinitely many > steps - and more are not feasible.
The only thing one needs to prove WM wrong is the proof that every listing of binary sequences is provably incomplete. > > There remain two possibilities: > Either there is no list of all lists including all their anti- > diagonals. This case is tantamount to there being not all steps to > infinity. Every |N includes all the "steps" to infinity, at least outside of WMYTHEOLOGY, so this claim is false
> Or there is this countable list containing all its antidiagonals.
When WM actually produces such a list explicitly, it will only then be believable, but he can't because there is on such list.
At least none outside his WMytheological Dreamland.
> Then > Cantor's argument fails because this list cannot be diagonalized.
Since it does not even exist, one may claim anything and everything about it. Including that even though it cannot be "diagoalized" it can be anti-diagonalized. > > In both cases there is nothing uncountable. > > > One reason that no man can have a list of all reals is that any such > > list provides the proof of its own incompleteness. > > So where and in which form *exist* all reals?
Most of them only outside WMytheology. > > Regards, WM --