Date: Jan 27, 2013 4:27 AM
Author: Virgil
Subject: Re: ZFC and God

In article 
<7760d43f-8d52-4675-a42b-f8bda2f6735e@4g2000yqv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> The reason for this uncertainty is the
> fact, that the Binary Tree constructed by all finite paths cannot be
> distinguished by digits (i.e. without further definition) from that
> Binary Tree that contains all infinite paths too.


They can, nevertheless, easily be distinguiched, because in binary tree
in which all paths are finite there will only be finitely many nodes. At
least if WM's paths satisfy the usual definition of being paths:

A path in a binary tree, at least of the types of trees we have been
talking about is by definition a maximal parent-child connected chain of
nodes.

Note that this standard definition prevents any path from being a proper
subset of any other path.

And in any binary tree in which paths are all finite in length (number
of nodes), there are also only finitely many paths and finitely many
nodes.

While this is obvious and clear to most others, it seem to be curiously
obscure to WM.
--