Liouville number

English

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

Liouville number (plural Liouville numbers)

(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 ${\\displaystyle \\textstyle 0<\\left|x-{\\frac {p}{q}}\\right|<{\\frac {1}{q^{n}}}.}$

单词	Liouville number
释义	Liouville number English Etymology Named after Joseph Liouville (1809–1882), a French mathematician. Noun Liouville number (plural Liouville numbers) (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 ${\\displaystyle \\textstyle 0<\\left\|x-{\\frac {p}{q}}\\right\|<{\\frac {1}{q^{n}}}.}$ Hypernyms transcendental number Related terms Liouville-Arnold theorem Liouville's equation Liouville's formula Liouville's theorem
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