On 13 Dez., 20:17, Virgil <vir...@ligriv.com> wrote: > In article > <f46dba51-46fc-4354-985c-27665000d...@x3g2000yqo.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> 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
moreover, they cannot be treated in a Cantor list.
> 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.
Explicit construction is onyl possible if every list number is defined. That restricts the constructed diagonals to a countable set. > > Thus it is your alleged set of all defineable/constructable paths that > either does not exist at all or is not countable.
You say it: The set of all definable real numbers is not countable. You just admitted a contradiction of set theory.