title: "Irrational Number"

Irrational Number

Definition. A real number is irrational if it is not rational: it cannot be written as $a/b$ with $a$ and $b$ integers and $b \neq 0$.

Irrationality proofs are typically by contradiction, because the negated claim hands you a concrete fraction to work with. The canonical example is $\sqrt{2}$ (Lecture 1, Example 5).