```Date: Apr 4, 2013 11:19 AM
Author: mueckenh@rz.fh-augsburg.de
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> paths.There is no need to say what numbers belong to mathematics - inmathematics. There is no need to say what paths belong to the BinaryTree - in mathemativs. Every path that you can form by unioning finitepaths 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 notchange, whether or not the Binary Tree is defined so or so.Regards, WM
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