Date: Mar 31, 2013 9:32 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <1qKdnWnmuLpMQMXMnZ2dnUVZ_qqdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 3/31/2013 1:44 PM, Virgil wrote:
> > In article
> > <3d98da78-e43c-4550-812c-6436200744ec@vh9g2000pbb.googlegroups.com>,
> > "Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> >

> >>>> 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.

> >>>
> >>> That is nonsense. 0.0101010101... has infinitely many of both sorts.
> >>>
> >>> Regards, WM

> >>
> >>
> >> Well, you see Virgil has introduced a term in context the "binary
> >> rational path"

> >
> > The standard definition of a binary rational is a rational whose
> > denominator is a power of 2.
> >
> > In binary place value notation, they are the infinite strings starting
> > at the binary point, then having onlybinary digits of 0 or 1, which end
> > with either a string of infinitely many 0's or infinitely many 1's.
> >
> > Thus in a Complete Infinite Binary Tree they correspond to infinite
> > paths with either only finitely many 1's or only finitely many 0's.
> >

>
>
> I will not disagree with your statement concerning "binary
> rational path", but I did do a search and did not come up
> with anything useful. That does not mean much since there
> are far more pages with "binary" and "rational" used in a
> context different from yours.
>
> I did, however, find dyadic rationals.
>
> http://en.wikipedia.org/wiki/Dyadic_rational
>
> These "standard terms" are sometimes a pain.
>
> What is important is that they are a dense subset
> in spite of not being the entire class of rational
> numbers.


If "binary rational" is only my own phraseology, it is still at least
unambiguously defined above.
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