Chapter 11.1, Problem 4E

Interpretation Introduction

Interpretation:

To show that the set of all real numbers whose decimal expansion contains only $\text{2’s and 7’s}$ is uncountable, by using Cantor’s diagonal argument.

Concept Introduction:

• If a set $\text{X}$ is in one-to-one correspondence with the set of natural numbers, then $\text{X}$ is said to be countable. Otherwise $\text{X}$ is uncountable.