Definition:Liouville Number

Definition
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:


 * $0 < \left \lvert x - \dfrac p q \right \rvert < \dfrac 1 {q^n}$

Also see

 * Liouville's Theorem (Number Theory)
 * Set of Liouville Numbers is Uncountable
 * Definition:Liouville's Constant