In article <email@example.com>, William Hughes <firstname.lastname@example.org> wrote:
> On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote: > > > 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 > > However, you keep talking about two types of paths, > paths with a last node and paths without a last node. > You have to say which subsets of nodes correspond to > paths. > > > > - in mathemativs. Every path that you can form by unioning finite > > paths is of course a path of the Binary Tree. > > Nope, you can form a subset of nodes without a last node > by unioning finite paths. You have to decide if you wish > to call this set of nodes a path.
WM invented a name "FISONs" for finite initial sets of naturals, and the set of naturals is naturally a Complete Infinite Unary Tree (CIUT) with one and only one "path" which is |N itself.
So what WM calls paths in a CIBT (Complete Infinite Binary Tree), are really only FISONs (finite initial sets of nodes) in that CIBT while paths are all infinite. --