Last Updated
：2025/11/30
Liouville number
Noun
Japanese Meaning
数論において、任意の正の整数 n に対し、q > 1 となる整数 q と適当な整数 p が存在し、0 < |x - p/q| < 1/(qⁿ) となる無理数を指す。
（ plural ）
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(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 0<|x-p/q|<1/(qⁿ).
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Liouville number
A Liouville number can be approximated by rational numbers far more closely than any algebraic irrational, which is why every Liouville number is transcendental.
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A Liouville number can be approximated by rational numbers far more closely than any algebraic irrational, which is why every Liouville number is transcendental.
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