Date: Dec 13, 2012 2:28 PM
Subject: Re: On the infinite binary Tree
On 13 Dez., 20:17, Virgil <vir...@ligriv.com> wrote:
> In article
> 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.