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 \(R\).



  • Mathematics

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