Look up inverse in Wiktionary, the free dictionary.

Inverse (logic), a type of immediate inference from a conditional sentence
Inverse (program), a program for solving inverse and optimization problems
Inverse multiplexer (or 'demultiplexer'), which breaks a single data stream into several streams with lower data rates
"Invert", a term used in the exotic pet industry to refer to arthropods
Inversions (novel), a science fiction novel by Iain M. Banks

Science, engineering and mathematics [link]

Inverse (mathematics)
Inversive geometry, transformation geometry based on inversion in a circle
Inverse problem, in science and mathematics, fitting a model to known data
Multiplicative inverse, a set of numbers which when multiplied yield the multiplicative identity, 1
Invert, the bottom of a sewer or tunnel, particularly if masonry lined. It may be flat or form a continuous curve with the tunnel arch.

https://wn.com/Inverse

Inverse (mathematics)

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.

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 or reciprocal of x is x⁻¹.
inverse function — inverse element with respect to function composition: a function that "reverses" the action of a given function: f⁻¹(f(x)) = x.

the additive inverse of x is −x;

the multiplicative inverse or reciprocal of x is x⁻¹.

inverse function — 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 — a geometric transform.

Circle inversion — another particular geometric transformation of a plane that maps the outside of a circle to the inside and vice versa.

Inverse limit — a notion in abstract algebra.

Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure involved, these definitions coincide in a group.

The word 'inverse' is derived from Latin: inversus that means 'turned upside down', 'overturned'.

Formal definitions

In a unital magma

Let $S$ be a set with a binary operation $*$ (i.e., a ~~magma~~ note that a magma also has closure under the binary operation). If $e$ is an identity element of $(S,*)$ (i.e., S is a unital magma) and $a*b=e$ , then $a$ is called a left inverse of $b$ and $b$ is called a right inverse of $a$ . If an element $x$ is both a left inverse and a right inverse of $y$ , then $x$ is called a two-sided inverse, or simply an inverse, of $y$ . An element with a two-sided inverse in $S$ is called invertible in $S$ . An element with an inverse element only on one side is left invertible, resp. right invertible. A unital magma in which all elements are invertible is called a loop. A loop whose binary operation satisfies the associative law is a group.

Contents

Science, engineering and mathematics [link]

See also [link]

https://wn.com/Inverse

Inverse (mathematics)

Inverse element

Formal definitions

In a unital magma

Podcasts:

EXPLORE WN.com