A map is called bijective if it is both injective and surjective. A bijective map is also called a bijection. A function admits an inverse (i.e., " is invertible") iff it is bijective.

Two sets and are called bijective if there is a bijective map from to . In this sense, "bijective" is a synonym for "equipollent" (or "equipotent"). Bijectivity is an equivalence relation on the class of sets.