Liouville number
id:
liouville-number-188-1036126
title:
Liouville number
text:
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers with q > 1 such that
- 0 < | x − p q | < 1 q n. The inequality implies that Liouville numbers possess an excellent sequence of rational number approximations. In 1844, Joseph Liouville proved a bound showing that there is a limit to how well algebraic numbers can be approximated by rational numbers, and he defined Liouville numbers specifically so that t
brand slug:
wiki
category slug:
encyclopedia
description:
Class of irrational numbers
original url:
https://en.wikipedia.org/wiki/Liouville_number
date created:
2002-05-01T00:15:10Z
date modified:
2024-09-08T20:44:17Z
main entity:
{"identifier":"Q1755697","url":"https://www.wikidata.org/entity/Q1755697"}
image:
fields total:
13
integrity:
15