Basic terminology and notation for functions
- Let A and B be sets. A function f from A to B is an assignment
of exactly one element of B to each element of A.
- We write f: A? B to indicate that f is a function from A to B;
we also say that f maps A to B.
- A is called the domain of f, and B is called the codomain of f.
- We write f(a)=b if b is the unique element of B assigned by the
function f to the element a of A; b is called the image of a, and a is a
- The range of f is the set
of all images of elements of A.
Range can be smaller than domain!