# 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:

$0 < \size {x - \dfrac p q} < \dfrac 1 {q^n}$

## Source of Name

This entry was named for Joseph Liouville.