# Inverse (mathematics)

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Inverse (mathematics)

Inverse is the opposite of something. This word and its derivatives are used greatly in mathematics, as illustrated below.
* Inverse element of an element "x" with respect to a binary operation * with identity element "e" is an element "y" such that "x" * "y" = "y" * "x" = "e". In particular,
**the additive inverse of "x" is –"x";
**the multiplicative inverse of "x" is "x"–1.
** Inverse function &mdash; inverse element with respect to function composition: a function that "reverses" the action of a given function: "f"–1("f"("x")) = "x".
* Inversion in a point &mdash; a geometric transform.
* Circle inversion &mdash; another particular geometric transformation of a plane that maps the outside of a circle to the inside and vice-versa.
* Inverse limit &mdash; a notion in abstract algebra.
* Inverse (logic) &mdash; ~"p" → ~"q" is the inverse of "p" → "q".
* Inverse matrix &mdash; inverse element with respect to matrix multiplication.
* Pseudoinverse, a generalization of the inverse matrix.
* Inverse proportion, also "inversely proportional" &mdash; a relationship between two variables "x" and "y" characterized by the equation $y=k/x.$
* Inverse problem &mdash; the task of identifying model parameters from observed data; see for example
**inverse scattering,
**inverse kinematics,
**inverse dynamics.
* Inverse perspective &mdash; the further the objects, the larger they are drawn.
* Inversive ring geometry &mdash; classical projective geometry extended by ring theory
* Inverse-square law &mdash; the magnitude of a force is proportional to the inverse square of the distance.
* Inverse transform sampling method &mdash; generate some random numbers according to a given probability distribution.
* Inverse chain rule method &mdash; related to integration and differentiation.
* Inversion of elements, a pair of adjacent out-of-order elements of a permutation (viewed as a list).
* Inverse relation

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