 The modern theory of infinities of counting derives from Cantor (1932). He observed that a natural way to set up a bijection between finite sets is to order the elements of each set, and pair the first element of one set with the first of the other, the second of one set with the second of the other, and so on. This sometimes works with infinite sets—for example, it gives the one-to-one correspondence between the natural numbers and the squares (considered under their standard ordering). When there is a one-to-one correspondence between two sets, such that every pair of elements of one set bears the same ordering as the corresponding pair of elements of the other set, the two ordered sets are said to have the same order type.