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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