Irrational Numbers

Cannot be expressed as p/q. Decimal expansion is non-terminating and non-repeating. Proof that √2 is irrational: Assume √2 = p/q (in lowest terms). Then 2 = p²/q². So p² = 2q² → p is even. Let p=2m. Then 4m² = 2q² → q²=2m² → q is even. But p and q both even contradicts lowest terms. Contradiction! ∴ √2 is irrational.