In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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?
Undefineable or unreconstructable paths are not needed to prove uncountability because every list of defineable/constructable paths proves the existence, by explicit definition/construction of it, of a path which has been omitted from that list.
Thus it is your alleged set of all defineable/constructable paths that either does not exist at all or is not countable. --