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.