On Mar 30, 3:36 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 30 Mrz., 10:17, William Hughes <wpihug...@gmail.com> wrote: > > > On 24 Mrz., 18:09, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > > > The only difference is that in the second case you consider > > > > some subsets of the nodes to be paths, that are not considered > > > > to be paths in the first case. > > > > Well, that is a correct description. It implies that these additional > > > subsets cannot be distinguished by nodes from the finite subsets > > > Piffle. It is trivial to distinguish a subset that has a node > > at a last level from a subset that does not have a node > > at a last level. > > No, that is impossible if an infinite path consists of infinitely many > finite subsets.
Let the subset of nodes in the infinitely many finite subsets be Q.
Q is contained in both trees, is not a path in the Binary Tree that contains only all finite paths (Q does not have a node at a last level) but is a path in the Binary Tree that contains in addition all actually infinite paths.
The difference between the trees is not which subsets of nodes exist, but which subsets are considered to be paths.