Date: Mar 31, 2013 9:32 PM
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
> > <email@example.com>,
> > "Ross A. Finlayson" <firstname.lastname@example.org> 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.
> 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
If "binary rational" is only my own phraseology, it is still at least
unambiguously defined above.