```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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