Date: Apr 5, 2013 6:01 PM Author: William Hughes Subject: Re: Matheology § 224 On Apr 5, 10:56 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 5 Apr., 21:10, William Hughes <wpihug...@gmail.com> wrote:

>

>

>

>

>

>

>

>

>

> > On Apr 5, 10:43 am, WM <mueck...@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.

>

> > Certainly the subset of nodes given by the union of a set

> > of FISONs exists,

>

> Of course it exists, namely in the tree according to the rules for

> paths. Therefore I do not have to assert its existence.

>

> > but since you won't say what makes a subset

> > of nodes a path you cannot claim that this subset of nodes

> > is a path.

>

> Ridiculous! A node belongs to a path, if its predecessor belongs to a

> path. The only exception is the root node. Need I define what a

> predecessor is?

>

No, but you need to define what a path is

A path is a set of nodes such that ...