Identity function

An identity function is a function which maps a set S to itself. In particular, a function id maps any element (such as numbers) to themselves.

Written another way, is the function from X → X, f(x) = x, which maps every element x to itself.

In elementary math, the main example is f(x) = x with the set of numbers.

 Notation 
The function idS typically denotes the identify function of a set S, the S in the subscript denotes the set S.

 Algebraic properties 
Given two sets X and Y with function f from X → Y, we have the two identities idX and idY, as well, having "○" denote function composition. We have the following

Category:Functions and mappings
Category:Set theory