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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