I do not want to be shortened. The motivation for this is that I would prefer that someone has the ability to learn everything they need to know about relations just by reading the popup summary.

A relation is a set of tuples, all of which have the same

generalize the function_arity page to include general arity

arity. The inclusion of a tuple in a relation indicates that the components of the tuple are related. A set of

-tuples is called an

n

-ary relation. Sets of pairs are called binary relations, sets of triples are called ternary relations, etc.

Examples of binary relations include the equality relation on natural numbers ${(0, 0), (1, 1), (2, 2), . . .}$ and the predecessor relation ${(0, 1), (1, 2), (2, 3), . . .}$ . When a symbol is used to denote a specific binary relation ( $R$ is commonly used for this purpose), that symbol can be used with infix notation to denote set membership: $x R y$ means that the pair $(x, y)$ is an element of the set $R$ .