MathDB

A set

S

of rational numbers is ordered in a tree-diagram in such a way that each rational number

\frac{a}{b}

(where

a

and

b

are coprime integers) has exactly two successors:

\frac{a}{a+b}

and

\frac{b}{a+b}

. How should the initial element be selected such that this tree contains the set of all rationals

r

with

0 < r < 1

? Give a procedure for determining the level of a rational number

\frac{p}{q}

in this tree.

Problem Statement