Date: Jan 13, 2013 10:16 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 190
On 13 Jan., 00:26, Virgil <vir...@ligriv.com> wrote:

> In article

> <4bffb7f3-9bfa-4dae-9108-da5e24389...@f4g2000yqh.googlegroups.com>,

>

>

>

>

>

> WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote:

> > > In article

> > > <c0615860-6190-4c10-9185-78ed2f6a2...@x10g2000yqx.googlegroups.com>,

>

> > > WM <mueck...@rz.fh-augsburg.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 Cantor-list belongs to a finite initial segments of the

anti-diagonal. There is nothing infinite that could explain or justify

uncountability.

Regards, WM