Date: Apr 1, 2013 8:14 PM
Subject: Re: Matheology � 224
WM <email@example.com> wrote:
> On 1 Apr., 15:19, William Hughes <wpihug...@gmail.com> wrote:
> > On Mar 30, 3:36 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 30 Mrz., 10:17, William Hughes <wpihug...@gmail.com> wrote:
> > > > On 24 Mrz., 18:09, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > <snip>
> > > > > > The only difference is that in the second case you consider
> > > > > > some subsets of the nodes to be paths, that are not considered
> > > > > > to be paths in the first case.
> > > > > Well, that is a correct description. It implies that these additional
> > > > > subsets cannot be distinguished by nodes from the finite subsets
> > > > Piffle. It is trivial to distinguish a subset that has a node
> > > > at a last level from a subset that does not have a node
> > > > at a last level.
> > > No, that is impossible if an infinite path consists of infinitely many
> > > finite subsets.
> > Let the subset of nodes in the infinitely many finite subsets
> > be Q.
> > Q is contained in both trees, is not a path
> > in the Binary Tree that contains only all
> > finite paths (Q does not have a node at
> > a last level)
> The path to which all finite paths
> contribute is a path too in the Binary Tree that contains all finite
In the COMPLETE INFINITE BINARY TREE, ther are no finite paths.
A FISON (finite initial sequence of nodes) in such a tree is never a
MISON (maximal initial sequence of nodes) and only a MISON can be a path
in a COMPLETE INFINITE BINARY TREE.
> There is no infinite path in the Binary Tree of all finite paths that
> would not be considered a path too.
But what WM calls paths are not paths in Complete Infinite Binary Trees.
> In other words: The Binary Tree of all finite paths
Is not ever a Complete Infinite Binary Tree.
What WM calls paths are not maximal, but in CIBT's they must be, by the
definition of CIBTs, maximal.
So that what WM chooses to call paths are not paths but merely FISONS.