Date: Apr 4, 2013 11:19 AM
Subject: Re: Matheology § 224
On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote:
> 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 shown
> me a set of nodes, but have not
> told me which subsets are considered
There is no need to say what numbers belong to mathematics - in
mathematics. There is no need to say what paths belong to the Binary
Tree - in mathemativs. Every path that you can form by unioning finite
paths is of course a path of the Binary Tree. Every node you point to,
is a node of a path, in fact even of a finite path. And this does not
change, whether or not the Binary Tree is defined so or so.