\begin{definition}[Definition:Real Number]
A working definition of the '''real numbers''' is as the set $\R$ which comprises the set of rational numbers $\Q$ together with the set of irrational numbers $\R \setminus \Q$.
It is admitted that this is a circular definition, as an irrational number is defined as a '''real number''' which is not a '''rational number'''.
More formal approaches are presented below.
\end{definition}