Relationship in which the elements are ordered-pairs.
In most contexts involved in primary and secondary education, the proposed relations are binary relations, that is, relations between two sets E and F, that are subsets of the Cartesian product \(E × F\).
In the same way that the elements of a binary relation are ordered pairs, the elements of a ternary relation are triples.
- All arithmetic operations are binary relations that associate an ordered pair of numbers with a result, based on a fixed rule. These operations can be defined as sets of ordered pairs whose elements are an ordered pair of numbers and a number. Therefore, for the operation of addition of whole numbers, we have the element ((2, 3), 5) which translates the operation 2 + 3 = 5.
- The unary operation of exponentiation can also be considered to be a binary relation in which every ordered pair (a, b) of numbers is made to correspond with a power denoted by ab : (2, 3) → 2³ = 8.