無理数(むりすう)

むりすう
noun
irrational number
number
1. irrational number
A real number that cannot be expressed as a ratio of two integers — examples include π (pi), √2, and e. Contrasted with rational numbers (有理数(ゆうりすう)).
円周率(えんしゅうりつ)は無理数(むりすう)だ。
Pi is an irrational number.
無理数(むりすう)は小数(しょうすう)で表(あらわ)すと無限(むげん)に続(つづ)く。
When written in decimal form, an irrational number continues infinitely.
√2が無理数(むりすう)であることは古代(こだい)ギリシャの時代(じだい)にすでに証明(しょうめい)されていた。
That √2 is irrational was already proven back in ancient Greek times.

Compound of 無理(むり) (impossible, unreasonable) + 数(すう) (number) — literally "unreasonable number," a calque of the European term. Used in mathematics from middle school onward.

Common collocations

Similar words

  • 有理数(ゆうりすう): rational number — direct antonym; expressible as a fraction
  • 実数(じっすう): real number — the broader category containing both rational and irrational numbers
  • 虚数(きょすう): imaginary number — numbers involving √-1, outside the real-number line

Related Words

Antonym: 有理数(ゆうりすう) (rational number)
Compare: 実数(じっすう) (real number)
general
Added 2026.6.8 17:30 · Revised 2026.9.2 13:02
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