# inverse

## English

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### Etymology

Recorded since 1440, from Latin inversus, the past participle of invertere ‎(to invert), itself from in- ‎(in, on) + vertere ‎(to turn).

### Pronunciation

•  Audio (US) (file)

inverse ‎(not comparable)

1. Opposite in effect, nature or order.
2. Reverse, opposite in order.
3. (botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
4. (mathematics) Having the properties of an inverse; said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity.
Multiplication is the inverse operation to division.
5. (linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.
6. (category theory) A morphism which is both a left inverse and a right inverse.

#### Translations

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.

### Noun

inverse ‎(plural inverses)

1. The opposite of a given, due to contrary nature or effect.
Deposing is the inverse of installing, and vice versa.
2. The reverse version of a procedure.
Removing one's shoes is the inverse of putting one's shoes on.
3. (mathematics, of an element x with respect to a binary operation) The element for which the operation, applied to it and x, yields the identity element of the operation.
The additive inverse of ${\displaystyle x}$ is ${\displaystyle -x}$, as ${\displaystyle x-x=0}$, where ${\displaystyle 0}$ is the additive identity element.
The multiplicative inverse of ${\displaystyle x}$ is ${\displaystyle x^{-1}}$, as ${\displaystyle x\times x^{-1}=1}$, where is ${\displaystyle 1}$ the multiplicative identity element.
The compositional inverse of a function ${\displaystyle f}$ is ${\displaystyle f^{-1}}$, as ${\displaystyle f\ f^{-1}={\mathit {I}}}$, where ${\displaystyle {\mathit {I}}}$ is the identity function (i.e., ${\displaystyle \forall x,f^{-1}(f(x))={\mathit {I}}(x)=x}$).
4. (logic) A statement constructed from the negatives of the premise and conclusion of some other statement.
${\displaystyle \lnot {\mathsf {p}}\to \lnot {\mathsf {q}}}$ is the inverse of ${\displaystyle {\mathsf {p}}\to {\mathsf {q}}}$.

#### Translations

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Help:How to check translations.

### Verb

inverse ‎(third-person singular simple present inverses, present participle inversing, simple past and past participle inversed)

1. (surveying) To compute the bearing and distance between two points.

## Dutch

Dutch Wikipedia has an article on:

Wikipedia nl

### Pronunciation

•  Audio (file)
• Hyphenation: in‧ver

### Noun

inverse m, f ‎(plural inversen)

inverse

## French

### Pronunciation

•  Audio (file)

inverse m, f ‎(plural inverses)

1. inverse, the other way round.

### Noun

inverse m ‎(plural inverses)

1. The inverse, the contrary

inverse