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:
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> > On Apr 5, 10:43 am, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 4 Apr., 21:01, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Apr 4, 8:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > On 4 Apr., 18:21, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > > > 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

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> > > > > > > > However, you keep talking about two types of paths,
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> > > > > > > Not at all. I talk about sets of nodes that are in the Binary Tree.
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> > > > > > Indeed, and some of these subsets of nodes are paths and
> > > > > > some are not.

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> > > > > In the Binary Tree there is no stop at any path.
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> > > > > > 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).

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

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

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

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> > Certainly the subset of nodes given by the union of a set
> > of FISONs exists,

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> Of course it exists, namely in the tree according to the rules for
> paths. Therefore I do not have to assert its existence.
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> > 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.

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> 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?
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No, but you need to define what a path is

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