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:

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

Also see

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

Source of Name

This entry was named for Joseph Liouville.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Liouville number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Liouville number
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Liouville number