One-to-One Correspondence

in mathematics, the correspondence between elements of two sets such that each element of the first set corresponds to a specific element of the second set and each element of the second set corresponds to a specific element of the first set. A one-to-one correspondence is a particular form of a function or mapping, in which the given function and its inverse are single-valued. If a one-to-one correspondence can be established between two sets, then these sets are equivalent. For example, the sets of integers and their squares are equivalent since the correspondence n → n² is a one-to-one correspondence.