Chapter 11.2, Problem 4E

Interpretation Introduction

Interpretation:

To find the measure of the set of irrational numbers between $\text{0}$ and $\text{1}$.

If it is countable or uncountable is to be found.

If it is fully disconnected is to be found.

If it contains any isolated points is to be found.

Concept Introduction:

• The rational numbers between $\text{0}$ and $\text{1}$ have the measure $\text{0}$.

• The real numbers are uncountable.

• A totally disconnected set means the set of irrational numbers does not contain any intervals.

• The isolated points are defined for a countable set.