Chapter 11.1, Problem 7E

Interpretation Introduction

Interpretation:

To show binary shift map ${\text{x}}_{\text{n+1}}{\text{= 2x}}_{\text{n}}(\mathrm{mod}\text{1)}$ have countably many periodic orbits and uncountably many aperiodic orbits.

Concept Introduction:

• For set of natural number $\text{N ={1,2,3,4,}\mathrm{...}\text{}}$ is any another set X can be put into one-to-one correspondence with the natural numbers then X is said to be countable if not then X is said to be uncountable.