Definition:Irrational Number

Definition
A real number which is not rational is irrational.

That is, an irrational number is one that can not be expressed in the form $\dfrac p q$ such that $p$ and $q$ are both integers.

The set of irrational numbers can therefore be expressed as $\R \setminus \Q$, where:
 * $\R$ is the set of real numbers
 * $\Q$ is the set of rational numbers
 * $\setminus$ denotes set difference.

Also see

 * Square Root of 2 is Irrational: that such numbers exist was known to the ancient Greeks.