Chapter 11.2, Problem 2E

Interpretation Introduction

Interpretation:

To show that rational numbers have zero measure.

Concept Introduction:

• To show that the rational numbers have zero measure, list the rational numbers and cover the first number with an interval length $\text{ε}$, cover the second number with an interval length of $\text{ε}\left(\frac{\text{1}}{\text{2}}\right)$ .

• The length of the set $\text{L}$ is $\text{L = ε - }\left({\text{a}}_{\text{1}}{\text{ + a}}_{\text{2}}{\text{ + a}}_{\text{3}}\text{ +}\mathrm{....}\right)$.