Correspondence
A one-to-one correspondence, or bijection, is a function which is both injective (or one-to-one) and surjective (or onto). A function is invertible exactly when it is a bijection.
One-to-one correspondences are useful in a variety of contexts. In particular, bijections are frequently used in combinatorics in order to count the elements of a set whose size is unknown. Bijections are also very important in set theory when dealing with arguments concerning infinite sets.
