```Date: Apr 1, 2013 6:14 PM
Author: William Hughes
Subject: Re: Matheology § 224

On Apr 1, 10:54 pm, WM <mueck...@rz.fh-augsburg.de> 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> 0.1> 0.11> 0.111> ...> contribute is a path  too in the Binary Tree that contains all finite> paths.Nope.  This set of nodes has no node at a last level.Every path in the Binary tree that contains all finite pathshas a node at a last level.The difference between the trees is not whichsubsets of nodes exist, but which subsets areconsidered to be paths.  Only in one of the treescan a subset of nodes with no node at a lastlevel be considered a path.
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