# Relation

comment: 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 arityarity. The inclusion of a tuple in a relation indicates that the components of the tuple are related. A set of $$n$$-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: $$xRy$$ means that the pair $$(x,y)$$ is an element of the set $$R$$.

Children:

Parents:

• Mathematics

Mathematics is the study of numbers and other ideal objects that can be described by axioms.