Formally, a relation over the sets X_{1}, ..., X_{n} is an n+1ary tuple R=(X_{1}, ..., X_{n}, G(R)) where G(R) is a subset of X_{1} × ... × X_{n} (the Cartesian product of these sets). G(R) is called the graph of R and, similar to the case of binary relation, R is often identified as its graph.
An nary predicate is a truthvalued function of n variables.
Because a relation as above defines uniquely an nary predicate that holds for x_{1}, ..., x_{n} iff (x_{1}, ..., x_{n}) is in R, and vice versa, the relation and the predicate are often denoted with the same symbol. So, for example, the following two statements are considered to be equivalent:
Relations are classified according to the number of sets in the Cartesian product; in other words the number of terms in the expression:
Relations with more than 4 terms are usually called called nary; for example "a 5ary relation".
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