Date: Apr 4, 2013 2:48 PM
Subject: Re: Matheology � 224
William Hughes <email@example.com> 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
> > - 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.