- #1

roadrunner

- 103

- 0

## Homework Statement

For every dyadic number q, find it's birthday

## Homework Equations

A dyadic rational is a number of the form n/2^k where n and k are integers.

Day 0: On day zero, the number 0 is born, and we identify 0 with fjg which we think of as

a split of the empty set into two empty sets.

Day n + 1: On day n + 1 we take all the numbers that have been born on days 0; 1; : : : n,

and we consider all possible ways to split these numbers into two sets fL j Rg where every

x 2 L and y 2 R satisfy x < y (note that we also allow L or R to be empty). We call L

the Left set and R the Right set. For each such split, a new number is born. If both L

and R are nonempty, then this new number is halfway in between the largest element of L

and the smallest element of R. If R is empty, then the new number is the smallest counting

number (positive integer) greater than everything in L, and similarly, if L is empty, we get

the largest negative counting number smaller than everything in R.

## The Attempt at a Solution

I really have no idea where to start..