Date: Jan 14, 2013 5:09 PM
Author: Virgil
Subject: Re: Matheology � 191
In article

<a5c980e5-9d27-4b95-8ecd-28935581cc1a@w3g2000yqj.googlegroups.com>,

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

> On 13 Jan., 23:44, Virgil <vir...@ligriv.com> wrote:

>

>

> > > 0.

> > > 0.0

> > > 0.1

> > > 0.00

> > > 0.01

> > > 0.10

> > > 0.11

> > > ...

> >

> > Since every path of a Complete Infinite Binary Tree must have infintely

> > many nodes (or, equivalently, infinitely many branchings), your list of

> > finite objects contains none of them

>

> Which node of what path is missing?

It is sets of nodes and sets of paths which are missing, not merely

individual nodes or paths. And which paths are be missing cannot be

determined without a list of those paths which are included.

On does not have set of nodes being a complete path in a Complete

Infinite Binary Tree until the root node is in the set and for each node

in the set one and only one of its child nodes is also in the set.

Thus only infinite sets of nodes can represent (complete) paths in a

Complete Infinite Binary Tree. Any finite set of nodes in a Complete

Infinite Binary Tree either does not all lie in any one path or all lies

in uncountably many paths, as many as in the whole tree.

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