Functions and Relations

We call A the domaindomain of a function of f. Since by the definition of a function, for each \(a\in A\) there is a unique b such that \((a, b)\in f\) , we write f(a) for b. The set \(\{f(a): a\in A\}\) is called the rangerange of a function of f. Mainly using the replacement axiom of ZF, it can be shown easily that the domain and the range of a function are sets. From now on, we shall take such facts for granted without mention. If B is any set containing the range of f, we write \(f: A\rightarrow B\) and say that f is a function or a map from A to B.