Encyclopedia > Identity map

  Article Content

Identity function

Redirected from Identity map

An identity function f is a function which doesn't have any effect: it always returns the same value that was used as its argument.

Formally, if M is a set, we define the identity function idM on M to be that function with domain and codomain M which satisfies

idM(x) = x    for all elements x in M.

If f : M → N is any function, then we have f o idM = f = idN o f. In particular, idM is the identity element of the monoid of all functions from M to M.

When choosing M equal to the positive integers, one obtains the identity function Id(n), which is a multiplicative function considered in number theory.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Quadratic formula

... formula is derived by the method of completing the square[?]. <math>ax^2+bx+c=0</math> Dividing our quadratic equation by a, w ...

This page was created in 38.4 ms