```Date: Dec 13, 2012 2:28 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: On the infinite binary Tree

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 neededmoreover, 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 isdefined. 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.Regaeds, WM
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