
Re: Matheology § 190
Posted:
Jan 13, 2013 10:16 AM


On 13 Jan., 00:26, Virgil <vir...@ligriv.com> wrote: > In article > <4bffb7f39bfa4dae9108da5e24389...@f4g2000yqh.googlegroups.com>, > > > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <c061586061904c10918578ed2f6a2...@x10g2000yqx.googlegroups.com>, > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > > > Matheology 190 > > > > > The Binary Tree can be constructed by aleph_0 finite paths. > > > > > 0 > > > > 1, 2 > > > > 3, 4, 5, 6 > > > > 7, ... > > > > Finite trees can be built having finitely many finite paths. > > > A Complete Infinite Binary Tree cannot be built with only finite paths, > > > as none of its paths can be finite. > > > Then the complete infinite set N cannot be built with only finite > > initial segments {1, 2, 3, ..., n} and not with ony finite numbers 1, > > 2, 3, ...? Like Zuhair you are claiming infinite naturals! > > A finite initial segment of N is not a path in the unary tree N. > > And neither N as a unary tree nor any Complete Infinite Binary Tree > has any finite paths. > > "A Complete Infinite Binary Tree cannot be built with only > finite paths, as none of its paths can be finite." > > Means the same as > > "A Complete Infinite Binary Tree cannot be built HAVING only > finite paths, as none of its paths can be finite." > > WM has this CRAZY notion that a path in a COMPLETE INFINITE BINARY TREE > can refer to certain finite sets of nodes. > > And no one is claiming any infinite naturals, only infinitely many > finite naturals.
So each n belongs to a finite initial segment (1,2,3,...,n). Same is valid for the nodes of the Binary Tree: Each node belongs to a finite initial segment of a path, the natural numbers (1,2,3,...,n) denoting the levels which the nodes belong to.
Everything in this model is countable. All finite initial segments belong to a countable set. Everything that possibly differs from an entry of a Cantorlist belongs to a finite initial segments of the antidiagonal. There is nothing infinite that could explain or justify uncountability.
Regards, WM

