Identity function
function that always returns the same value that was used as its argument
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
changeThe function idS typically denotes the identify function of a set S, the S in the subscript denotes the set S.
Algebraic properties
changeGiven 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
