Finitary relation

In mathematics, a finitary relation over a sequence of sets X₁, ..., X_n is a subset of the Cartesian product X₁ × ... × X_n; that is, it is a set of n-tuples (x₁, ..., x_n), each being a sequence of elements x_i in the corresponding X_i. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true.

The non-negative integer n that gives the number of "places" in the relation is called the arity, adicity or degree of the relation. A relation with n "places" is variously called an n-ary relation, an n-adic relation or a relation of degree n. Relations with a finite number of places are called finitary relations (or simply relations if the context is clear). It is also possible to generalize the concept to infinitary relations with infinite sequences.

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