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 - 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.