Involution

:See involution (philosophy) for the philosophy meaning.

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In mathematics, an involution, or an involutary function, is a function that is its own inverse, so that

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:f(f(x)) = x for all x in the domain of f.

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The identity map is a trivial example of an involution. Common examples in mathematics of more interesting involutions include multiplication by −1 in arithmetic, the taking of reciprocals, complementation in set theory and complex conjugation.

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Another kind of inversion which is also an involution is circle inversion, which is a mapping of the plane into itself, which exchanges the interior and the exterior of a circle and takes the role in inversive geometry of the reflection in Euclidean geometry. In the complex plane it corresponds to taking the conjugate of the reciprocal.

Function: In general (not in the mathematical but in the engineering sense), a function is a goal-oriented property of an entity. The carrier of a function is a process; therefore, is possible to realise the same function using different physical processes, and one process can be a carrier of multiple funct...

Inverse: Inverse typically means the opposite of something....

Identity map: : This article is about the Identity Map software design pattern. For the mathematical concept, see Identity function....