CORRESPONDENCE (from med. scholastic Lat. correspondentia, correspondere, compounded of Lat. cum, with, and respondere, to answer; cf. Fr. correspondence), strictly a mutual agreement or fitness of parts or character, that which fits or answers to a requirement in another, or more generally a similarity or parallelism. In the 17th and 18th centuries the word was frequently applied to relations and communications between states. It is now, outside special applications, chiefly applied to the interchange of communications by letter, or to the letters themselves, between private individuals, states, business houses, or from individuals to the press. The “doctrine of correspondence or correspondences,” one of the leading tenets of Swedenborgianism, is that every natural object corresponds to and typifies some spiritual principle or truth, this being the only key to the true interpretation of Scripture. In mathematics, the term “correspondence” implies the existence of some relation between the members of two groups of objects. If each object of one group corresponds to one and only one object of the second, and vice versa, then a one-to-one correspondence exists between the groups. If each object of the first group corresponds to β objects of the second group, and each object of the second group corresponds to a objects of the first group, then an α to β correspondence exists between the two groups. For examples of the application of this notion see Curve.