Translation guide
The English word "inverse" is used in mathematics, logic, and general language to mean "opposite" or "reversed." In Japanese, the translation depends heavily on context. This guide covers the most common ways to express the idea of "inverse" for learners.
To refer to the inverse of a mathematical function, operation, or element.
Specifically means "inverse function." Use this when talking about the inverse of a function in mathematics.
fの逆関数はf^{-1}と書く。
The inverse function of f is written as f^{-1}.
Means "reciprocal" (multiplicative inverse) of a number. Use for 1/x.
2の逆数は1/2です。
The inverse of 2 is 1/2.
Means "inverse element" in abstract algebra (group theory). More technical.
群において、各元は逆元を持つ。
In a group, every element has an inverse.
Means "inverse matrix." Use in linear algebra.
この行列の逆行列を求めなさい。
Find the inverse matrix of this matrix.
To describe something that is the opposite or reverse of something else, often in a logical or relational sense.
The most common and versatile word for "inverse," "reverse," or "opposite." Can be used as a noun or prefix.
逆の方向に進んでください。
Please go in the opposite direction.
彼の意見は私のと逆だ。
His opinion is the opposite of mine.
Means "opposite" or "contrary." Often used for opposing ideas, directions, or positions.
Means "conversely" or "inversely speaking." Used to introduce a statement from the opposite perspective.
彼は怠け者だ。逆に言えば、効率的とも言える。
He is lazy. Conversely, you could say he is efficient.
Means "paradox." An inverse or contradictory statement that may be true.
To describe a relationship where one quantity increases as the other decreases.
Means "inverse proportion" or "inversely proportional." Used in mathematics and science.
圧力は体積に反比例する。
Pressure is inversely proportional to volume.
Means "inverse correlation" or "negative correlation." Used in statistics.
喫煙率と健康寿命には逆相関がある。
There is an inverse correlation between smoking rates and healthy life expectancy.
To refer to the inverse of a conditional statement in logic.
In logic, the inverse of "if P then Q" is "if not P then not Q." This is called 裏 (ura).
「PならばQ」の裏は「PでなければQでない」です。
The inverse of "if P then Q" is "if not P then not Q."
Sometimes 逆 (gyaku) is used loosely for the converse or inverse in everyday logic, but in formal logic, 逆 is the converse (Q → P), not the inverse.
In formal logic, 逆 means converse, not inverse. Use 裏 for inverse.
While 逆 (gyaku) is the most common translation, it can sound vague or unnatural in technical contexts. Use specific terms like 逆関数 (inverse function), 逆数 (reciprocal), or 反比例 (inverse proportion) when appropriate.
逆 (gyaku) often implies a reversal of order, direction, or logical relationship. 反対 (hantai) implies opposition or contrast. For example, 逆方向 (opposite direction) vs. 反対意見 (opposing opinion).
彼は反対の立場をとった。
He took the opposite stance.
「急がば回れ」は逆説だ。
"Haste makes waste" is a paradox.
In everyday conversation, "gyaku" is sometimes used to mean "ura" (inverse).