Partial function

In mathematics, a partial function from X to Y (written as ) is a function , for some subset X' of X. It generalizes the concept of a function by not forcing f to map every element of X to an element of Y (only some subset X' of X). If , then f is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X', is not known (e.g. many functions in computability theory).