Liouville number

Named after Joseph Liouville (1809–1882), a French mathematician.

Liouville number (plural Liouville numbers)

1. (number theory) An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that ${\displaystyle \textstyle 0<\left|x-{\frac {p}{q}}\right|<{\frac {1}{q^{n}}}.}$

• transcendental number

• Liouville-Arnold theorem
• Liouville's equation
• Liouville's formula
• Liouville's theorem