Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example $\text{11}\text{.1}\text{.4}$ show that the rationals are also uncountable?

Concept Introduction:

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

• The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.