In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 9 Dez., 10:16, Virgil <vir...@ligriv.com> wrote: > > > > See above. People have not taken into account that only a *defined* > > > sequence gives a defined diagonal. There are only countably many > > > finite definitions. > > > > Again: none of the paths in such a list of paths need be defined beyond > > a finite number of places in order to define an anti-diagonal provably > > not in that list. > > Wrong.
No WM! WM is, as usual, the one who is wrong!
The first path in the list need only be EXPLICITLY determined to the end of its first branch in order for the antidiagonal to that list to be made to differ from it. The second path in the list need only be EXPLICITLY determined to the end of its second branch in order for an antidiagonal to that list to be made to differ from it. And so on for the third path, fourth path,and so on ad infinitum. So that WM is wrong again, as usual!
>The list is infinite. If only a finite part of the list can be > excluded to contain the anti-diagonal, then nothing yet has been > proven. This holds for every finite part.
Any general rule, which applies equally well to any member of a list, applies to every member of an endless list just as well as to every member of a terminating list.
Note that the very definition of any set is by establishing a rule for distinguishing between members and non-members. What WM cannot see is that this rule need not be in the form of a finite list of members.
So that the set of binary sequences or paths in any list, being just an ordered set, is determined by some rule, and any such rule allows us to determine at least one non-member of such a list. --