```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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