English Dictionary

Liouville number

名詞

(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).

日本語の意味

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。

A Liouville number can be approximated by rational numbers far more closely than any algebraic irrational, which is why every Liouville number is transcendental.

リウヴィル数は、有理数で任意に高い精度で近似できるため、すべてのリウヴィル数は超越数になります。

意味（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 0<|x-p/q|<1/(qⁿ).

Liouville numbers （ plural ）