Date: Mar 31, 2013 2:44 PM
Subject: Re: Matheology � 224
"Ross A. Finlayson" <email@example.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.