Identity Property

When a set possesses an identity element for a given operation, the mathematical system of the set and operation is said to possess the identity property for that operation. For example, the set of all functions of a variable over the real numbers has the identity element, or identity function, I(x) = x. In other words, if f(x) is any function over the real numbers, then f(I(x)) = I(f(x)) = f(x).