Date: Apr 4, 2013 10:08 AM
Author: William Hughes
Subject: Re: Matheology § 224

On Apr 2, 10:45 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 2 Apr., 00:14, William Hughes <wpihug...@gmail.com> wrote:

> > The difference between the trees is not which
> > subsets of nodes exist, but which subsets are
> > considered to be paths.
>
> The tree of all finite paths and the tree of all paths like every tree
> has infinite paths. Therefore there is no tree which has only finite
> subsets that are considered paths.
>

You confuse subsets of nodes, which belong
to both trees, with paths which are defined
differently for the two different trees.
Only in one of the trees
can a subset of nodes without a last
node be considered a path.

>
> Is this tree
>
>     0.
>   0  1
> 0 1 0 1
> ...
>
> that one with infinite subsets not considered paths?

I do not know.  You have shows
me a set of nodes, but have not
told me which subsets are considered
paths.