# Inverse definition

ĭn-vûrs, ĭnvûrs
Inverted; reversed in order or relation; directly opposite.
An inverse is defined as a reverse or direct opposite, particularly in math.

An example of an inverse is 1/4 to 4.

noun
The definition of inverse is reverse or direct opposite.

An example of something inverse is the relationship between division and multiplication.

The result of an inversion.
noun
The result obtained after dividing 1 by the given number; reciprocal.

The inverse of x is 1/x.

noun
Relating to a mathematical operation whose nature or effect is the opposite of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
An inverse operation. Subtraction is the inverse of addition.
noun
Opposite in effect or nature or order.
Reverse, opposite in order.
(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.

(linguistics, Kiowa-Tanoan) A grammatical number marking that indicates the opposite grammatical number (numbers) of the default number specification of noun class.
(category theory) A morphism which is both a left inverse and a right inverse.
The opposite of a given, due to contrary nature or effect.

Deposing is the opposite of installing, and vice versa.

noun
The reverse version of a procedure.

Removing one's shoes is the inverse of putting one's shoes on.

noun
(mathematics) 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).

noun
(logic) A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.
noun
(surveying) To compute the bearing and distance between two points.
verb
(mathematics) One of a pair of elements in a set whose result under the operation of the set is the identity element, especially:
• The reciprocal of a designated quantity.
• The negative of a designated quantity.
noun
(mathematics) Of or relating to an inverse or an inverse function.
(archaic) Turned upside down; inverted.
Reversed in order, nature, or effect.
Either of a pair of elements in a set whose result under the mathematical operation of the set is the identity element. For example, the inverse of 5 under multiplication is1 /5 , since 5 ×1 /5 = 1, the identity element under multiplication. The inverse of 5 under addition is −5, since 5 + −5 = 0.
noun
Any inverse thing; direct opposite.
noun
(botany) Inverted; having a position or mode of attachment the reverse of that which is usual.
Something that is opposite, as in sequence or character; the reverse.
noun
(math.) Designating or of an operation which, when applied after a specific operation, cancels it.

Subtraction is the inverse operation of addition.

Singular:
inverse
Plural:

## Origin of inverse

• Middle English from Latin inversus past participle of invertere to invert invert

### From American Heritage Dictionary of the English Language, 5th Edition

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