\begin{definition}[Definition:Irrational Number]
An '''irrational number''' is a real number which is not rational.
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.
\end{definition}