Identity Function


The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map.

The identity function is trivially idempotent, i.e., id(id(x))=x.


The identity function f(z)=z in the complex plane is illustrated above.


A function that approximates the identity function for small x to terms of order O(x^5) is given by


(OEIS A115183 and A115184). This function leads to some nice pi approximations.

See also

Constant Function, Idempotent, Zero Function

Explore with Wolfram|Alpha


Sloane, N. J. A. Sequences A115183 and A115184 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Identity Function

Cite this as:

Weisstein, Eric W. "Identity Function." From MathWorld--A Wolfram Web Resource.

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