In mathematics, two sets A and B are equinumerous if there exists a one-to-one correspondence (a bijection) between them, i.e. if there exists a function from A to B such that for every element y of B there is exactly one element x of A with f(x) = y. Equinumerous finite sets have the same number of elements. The definition of equinumerosity using bijections can be applied to both finite and infinite sets and allows one to state whether two sets have the same size even if they are infinite. Unlike finite sets, some infinite sets are equinumerous to proper subsets of themselves.