Virgil
Posts:
4,674
Registered:
1/6/11
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Re: On the infinite binary Tree
Posted:
Dec 13, 2012 2:17 PM
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In article
<f46dba51-46fc-4354-985c-27665000dbf4@x3g2000yqo.googlegroups.com>,
WM <mueckenh@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 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.
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