```Date: Mar 30, 2013 6:45 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

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 initialsegments which are in the tree. But as you said, 1/pi is not distinctfrom them. It comes into tze construction automatically. The limit isin 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 saidthat the irrationals come into the tree automatically, impossible todistinguish by nodes.Regards, WM
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