Date: Mar 31, 2013 2:44 PM
Author: Virgil
Subject: Re: Matheology � 224
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.

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