Function as a Set of Ordered Pairs
Function as a set of ordered pairs
Let A and B be two non-empty sets. A relation f from A to B i.e a subset of A × B is called a function (or a mapping or a map) from A to B, if
i) for each a ∈ A there exists b ∈ B such that (a, b) ∈ f.
Thus, a non-void subset of A×B is a function from A to B if each element of A appears in some order pair in f and no two ordered pairs in f have the same first element.
If (a, b) ∈ f, then b is called the image of a under f.
