Liouville number

noun

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 0<|x-p/q|<1/(qⁿ).

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Meanings

nounLiouville number (plural Liouville numbers)

plural Liouville numbers

  1. mathematicsAn irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ).

Origin

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

Full word history & related roots →

Translations

Polish liczba Liouville'a
  • liczba Liouville'airrational number
Cite this entry
APA

Liouville number. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Liouville%20number

MLA

“Liouville number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Liouville%20number. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Liouville number,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Liouville%20number.

Source: Liouville number on Wiktionary, CC BY-SA 4.0.