Date: Mar 26, 2013 4:47 PM
Subject: Re: Matheology § 224
On 3/26/2013 3:00 PM, Virgil wrote:
> In article
> WM <firstname.lastname@example.org> wrote:
>> On 26 Mrz., 00:18, Virgil <vir...@ligriv.com> wrote:
>>> In article
>>> 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)
It just went over WM's head, as predicted.