In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set in the notation , and is alternatively denoted as formula_1. Since a function is defined on its entire domain, its domain coincides with its domain of definition. However, this coincidence is no longer true for a partial function, since the domain of definition of a partial function can be a proper subset of the domain.