Date: Mar 26, 2013 4:00 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<6eabd00e-1678-4e4e-8281-22b180dbca51@m12g2000yqp.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 26 Mrz., 00:18, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <ad404888-6726-4aa3-b421-fcc887b93...@7g2000yqy.googlegroups.com>,

> >

> > WM <mueck...@rz.fh-augsburg.de> wrote:

> > > So the set of all rational numbers always contains all irrational

> > > numbers? Or only some? Or is that a speciality of the Binary Tree?

> >

> > It is a speciality of a complete binary tree.

> >

> > It is something that would be fairly obvious to any competent

> > mathematician, which is, no doubt, why it is not obvious to WM.

> > --

>

> I let this stand as it is.

I should have said a Complete INFINITE Binary Tree.

There is no Complete INFINITE Binary Tree which can represent all binary

rationals in the interval [0,1] by paths without also having a path for

every limit of a convergent sequence of such binary rationals.

As any competent mathematician can easily verify for himself.

--