## INVERSE

### Inverse

In many contexts in mathematics the term**inverse**indicates the opposite of something. This word and its derivatives are used widely in mathematics, as illustrated below.

*The above text is a snippet from Wikipedia: Inverse (mathematics)*

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### inverse

#### Noun

- The opposite of a given, due to contrary nature or effect.
- ''Deposing is the
**opposite**of installing, and vice versa

- ''Deposing is the
- The reverse version of a procedure.
*Removing one's shoes is the***inverse**of putting one's shoes on

- The inverse of an element
*x*with respect to a binary operation is an element that when combined with*x*yields the appropriate identity element.*The additive***inverse**of x is -x as, x + -x = 0 where 0 is the additive identity element.*The multiplicative***inverse**of x is x^{-1}as, x * x^{-1}= 1 where 1 is the multiplicative identity element.- ''The compositional
**inverse**of a function f is f^{–1}as, f f^{–1}is the identity function (ie f^{–1}(f(a)) = a for all a).

- A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.

#### Verb

#### Adjective

- Opposite in effect or nature or order
- reverse, opposite in order
- Inverted; having a position or mode of attachment the reverse of that which is usual.
- 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.

- A grammatical number marking that indicates the opposite grammatical number (or numbers) of the default number specification of noun class.

*The above text is a snippet from Wiktionary: inverse*

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