Date: Mar 24, 2013 7:29 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<5e0e68cb-02d9-4397-8590-1655cb66c67c@9g2000yqy.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Mrz., 20:57, fom <fomJ...@nyms.net> wrote:
>

> > > Please answer this question (the best way for our readers to
> > > understand the difference between pot. and act. infinity):
> > > What is the difference between the Binary Tree that constains only all
> > > finite paths and the Binary Tree that contains in addition all
> > > actually infinite paths?

> >
> > The first does not exist.

>
> Another interesting opinion. But why does it not exist?


Either the tree is not a binary one, or it will necessarily contain at
least one infinite path

Here is the schematic for a binary tree with one and only one path of
each positive finite length.

Note that it also and necessarily has an infinite path of 0 nodes.

Root
| \
0 1
| \
0 1
| \
0 1
| \
0 1
| \
0 1
| \
0 1
| \
0 1
| \
0 1

and so on, ad infinitum, each 0 node having two children and each 1
having none.
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