\begin{definition}[Definition:Liouville Number]
A real number $x$ is a '''Liouville number''' if for all $n \in \N$, there exist $p, q \in \Z$ (which may depend on $n$) with $q > 1$ such that:
:$0 < \size {x - \dfrac p q} < \dfrac 1 {q^n}$
\end{definition}