Identity Function

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An Identity Function is an mathematical function defined as [math]\displaystyle{ f(x)=x }[/math].



References

2018

  • (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Identity_function Retrieved:2018-2-4.
    • In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. In equations, the function is given by f(x) = x.

      Definition

      Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies: f(x) = x   for all elements x in M.[1]

      In other words, the function value f(x) in M (that is, the codomain) is always the same input element x of M (now considered as the domain). The identity function on M is clearly an injective function as well as a surjective function, so it is also bijective.[2]

      The identity function f on M is often denoted by idM.

      In set theory, where a function is defined as a particular kind of binary relation, the identity function is given by the identity relation, or diagonal of M.


  1. Template:Citation
  2. Mapa, Sadhan Kumar. Higher Algebra Abstract and Linear (11th ed.). Sarat Book House. p. 36. ISBN 978-93-80663-24-1.