Proof by contradiction establishes the truth of a statement by showing that assuming that the statement to be false leads to a contradiction.

To prove something by contradiction:

1. Assume that the statement is not true.
2. Show that the consequences of this assumption leads to an impossible result.

You must be able to prove the following:

• Prove by contradiction that $\sqrt{2}$ is irrational.
• Prove by contradiction that the number of prime numbers is infinite.