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).
円周率は無理数だ。
Pi is an irrational number.
無理数は小数で表すと無限に続く。
When written in decimal form, an irrational number continues infinitely.
√2が無理数であることは古代ギリシャの時代にすでに証明されていた。
That √2 is irrational was already proven back in ancient Greek times.
Compound of 無理 (impossible, unreasonable) + 数 (number) — literally "unreasonable number," a calque of the European term. Used in mathematics from middle school onward.
COMMON COLLOCATIONS:
- 無理数と有理数: irrational and rational numbers
- 無理数を含む: to include irrational numbers
- 無限小数の無理数: irrational number as an infinite decimal
SIMILAR WORDS:
- 有理数: rational number — direct antonym; expressible as a fraction
- 実数: real number — the broader category containing both rational and irrational numbers
- 虚数: imaginary number — numbers involving √-1, outside the real-number line