Date: Apr 5, 2013 4:57 AM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<8fe0097d-9dbc-488f-8ccb-50cc12efb3ed@c7g2000vbe.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 4 Apr., 21:01, William Hughes <wpihug...@gmail.com> wrote:
> > On Apr 4, 8:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >

> > > On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 4 Apr., 18:21, William Hughes <wpihug...@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,
> >
> > > > > Not at all. I talk about sets of nodes that are in the Binary Tree.
> >
> > > > Indeed, and some of these subsets of nodes are paths and
> > > > some are not.

> >
> > > In the Binary Tree there is no stop at any path.
> >
> > > > You talk about subsets of nodes with a last node
> > > > and subsets of nodes without a last node.  However,
> > > > you refuse outright to indicate what makes a subset of nodes
> > > > a path  (certainly not all subsets of nodes are paths).

> >
> > > All nodes that belong to a finite path, belong to an infinite path
> > > too.

> >
> > Since you refuse to say what makes a subset of nodes a path
> > you cannot claim that a path without a last node exists.-

>
> I do not claim it. The infinite path, claimed or not, is simply
> existing as the union of all its FISONs.


Each FISON is a set, and in any set theory the union of a set of sets
is always itself set.

> There is no rule that
> prevents unioning FISONs and there is no last node.


Thus each path in any CIBT is an infinite sequence of nodes that is
order-isomorphic to the set of naturals, as required in ZF.
--