On 13 Dez., 09:26, Virgil <vir...@ligriv.com> wrote:
> > No. I proved that the number of infinite paths is countable by > > constructing all nodes of the Binbary Tree by a countable set of > > infinite paths. > > WM is again, or should I say still, self-deluded in all sorts of ways. > > The only way WM could actually have CONSTRUCTED all nodes of a INFINITE > binary tree is by completing infinitely many construction steps himself > which he has often claimed that no one can ever do.
If actual infinity exists (and I assume that for the sake of contradiction) then the CIBT can be constructed.
> Such trees can exist only in the imagination, as is the case with a > great many mathematical "constructions". > > But the set of paths of such an imagined tree, to be consistent, must > have a different path for every different subset of the set of all > naturals numbers, being the set of levels at which that path branches > left, and there are uncountably many such subsets of N.
Alas most of them are not definable. Why does no Cantor-list contain undefinable elements?