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. > > 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. --