# Relation

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:

- Equivalence relation
A relation that allows you to partition a set into equivalence classes.

- Order relation
A way of determining which elements of a set come “before” or “after” other elements.

- Transitive relation
If a is related to b and b is related to c, then a is related to c.

- Reflexive relation
- Antisymmetric relation
A binary relation where no two distinct elements are related in both directions

Parents:

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