```Date: Mar 30, 2013 9:09 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <4f5abe9e-4a74-4ada-ab2c-3f6cab383e3e@ia3g2000vbb.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 30 Mrz., 19:15, Virgil <vir...@ligriv.com> wrote:> > In article> > <ab85409a-eabf-4b68-b505-d194ed33a...@c15g2000vbl.googlegroups.com>,> >> >> >> >> >> >  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.> >> > All infinities consist of infinitely many finite parts.> > But the infinite set of all naturals is distinguishable be from the> > infinite set of all FISONs,> > And so is the path of 1/pi distinguishable from all its finite initial> segments which are in the tree. But as you said, 1/pi is not distinct> from them. WM conflates the set of all FISONs with the union of that set, |N, so, as he does far too often, fails to distinguish between the subsets of a set and the members of a set.Until he has learned ro  distinguish between the members of a set and the subset of a set reliably, he should avoid anything to do with sets. It comes into tze construction automatically. The limit is> in any case a member of the sequence. That is unmathematical.> >> > > It is impossible to distinguish the actually infinite path of 1/pi> > > from a path that only is built of all finite initial segments of the> > > path of 1/pi.> >> > It may be so in Wolkenmuekenheim, but a set of only finite> > approximations to an irrational number can elsewhere be distinguished> > from the number itself.> > Then explain why this is not possible in the Binary Tree. You said> that the irrationals come into the tree automatically, impossible to> distinguish by nodes.I never said that they were impossible to distinguish by node, because they are. In a Complete Infinite Binary Tree, every binary rational path has only finitely many left-child nodes or only finitely many right-child nodes, whereas every other path has infinitely many of each.Something that everyone who understands anything about Complete Infinite Binary Trees should know but WM apparently does not.--
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