Date: Apr 4, 2013 2:48 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<379e1105-d549-4ded-8378-3ec07cb04bc7@o9g2000vbk.googlegroups.com>,
William Hughes <wpihughes@gmail.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
> 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.
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