Much of mathematics is about finding a pattern - a recognisable link between quantities that change. In our daily life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student.
In mathematics also, we come across many relations such as number m is less than number n, line l is parallel to line m, set A is a subset of set B. In all these, we notice that a relation involves pairs of objects in certain order.
Ordered pair: A pair of elements grouped together in a particular order.
Relation: A relation R from a set A to a set B is a subset of the cartesian product A × B obtained by describing a relationship between the first element x and the second element y of the ordered pairs in A × B.
The domain of R is the set of all first elements of the ordered pairs in a relation R. The range of the relation R is the set of all second elements of the ordered pairs in a relation R.
Function: A function f from a set A to a set B is a specific type of relation for which every element x of set A has one and only one image y in set B.
We write f: A→B, where f(x) = y.
A is the domain and B is the codomain of f. A real function has the set of real numbers or one of its subsets both as its domain and as its range.