# Prove the set of irrational numbers is uncountable.

## Homework Statement

Prove the set of irrational numbers is uncountable.

## The Attempt at a Solution

We proved that the set [0,1] is uncountable, but I'm not sure how to do it for the irrational numbers.

1) The set $\mathbb{Q}$ of rational numbers is countable.
2) The set $\mathbb{R}$ of real numbers is uncountable.