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From Wikipedia, the free encyclopedia

In mathematics an identity function is a function which maps each of the arguments or inputs to itself. More formally, a function f : A → A, is an identity function if f(x) = x for all x in A. For each set A, there is a unique such function, and it is called the identity function on A, and is often denoted id_A or 1_A.

[edit] Properties

Identity functions can be characterized with respect to function composition in two way.

The following are equivalent:

• f is the identity function on A.
• For all functions g with domain A, f o g = g.
• For all functions h with codomain A, h o f = h.