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. --