Date: Mar 26, 2013 4:47 PM
Author: fom
Subject: Re: Matheology § 224
On 3/26/2013 3:00 PM, Virgil wrote:

> 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.

>

In spite of the apparent need for the additional

adjective, the context of

(rational numbers + irrational numbers + binary tree)

sufficed.

It just went over WM's head, as predicted.