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.

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