1.
in mathematics, any number that can be represented as a point on the number line, including rational numbers (such as 1/2 or -3) and irrational numbers (such as √2 and π); a real number
The mathematical term for the full set of numbers on the continuous number line, excluding only the imaginary and complex numbers. The real numbers include integers, fractions, and non-terminating decimals such as π and √2. Introduced in Japanese high-school mathematics when the number system is extended beyond rationals. The set is written ℝ, which in Japanese textbooks is usually explained as 'the set of all 実数.'
2.
the actual number or actual count of people, things, or events, as opposed to an estimated, listed, or nominal figure; the real number, the actual count
In everyday usage, 実数 refers to the real, actual count of something — how many people actually showed up, how many copies were actually sold, how many cases actually occurred — as opposed to planned, rounded, publicly announced, or rate-based figures. Often contrasted with percentages, ratios, or official estimates.
Composed of 実 ('real, actual, true') + 数 ('number'). The two meanings — 'real number' (math) and 'actual count' (everyday) — share the same underlying idea of 'real / actual number.'
COMMON COLLOCATIONS (Sense 1 — math):
- 実数の集合: the set of real numbers
- 実数解: real(-valued) solution
- 実数全体: all of the real numbers (as a set)
- 負の実数: negative real number
- 実数の範囲で: within the real numbers (standard math phrasing)
COMMON COLLOCATIONS (Sense 2 — everyday):
- 実数を把握する: to grasp the actual numbers
- 実数で示す: to show in actual figures
- 実数と割合: actual number and percentage
- 参加者の実数: the actual number of participants
- 実数ベース: on an actual-numbers basis
Math number systems
- 自然数: natural numbers (1, 2, 3, ...)
- 整数: integers (..., -1, 0, 1, 2, ...)
- 有理数: rational numbers (fractions)
- 無理数: irrational numbers (√2, π, ...)
- 実数: real numbers (rational + irrational)
- 虚数: imaginary numbers
- 複素数: complex numbers (real + imaginary)
Similar words
- 実数値: actual numerical value — often used interchangeably with sense 2, especially in statistics.
- 総数: total number — the overall count.
- 正味: net amount — actual amount after subtracting what does not count.
- 実勢価格: the actual market price (as opposed to list price) — uses 実 in a related 'real / actual' sense.
Antonyms / contrasts
- (Sense 1) 虚数: imaginary number.
- (Sense 2) 割合 / 比率: percentage / ratio — the abstract rate shown instead of an actual count.
- (Sense 2) 推計: estimated figure — the calculated estimate that 実数 is being contrasted with.
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Sense 1 is technical and confined to mathematics. Sense 2 is neutral and widely used in journalism, business, statistics, and everyday conversation.
Related Words
Compare:
総数 (total number)
Compare:
正味 (net amount)
Related:
有理数 (rational number)
Compare:
小数 (decimal)
Compare:
無理数 (irrational number)