Definitions

DEFINITION 1 The statement that X is a subset of Y means that if p is an element of X, then p is and element of Y.

DEFINITION 3. The statement that f is a function from X into Y means that
1. f is a subset of $X \times Y$
2. if p is an element of X, then there is an element of f so that its first coordinate is p,
and
3. if (a,b) is an element of f and (a,c) is an element of f, then b = c.

math IS fun

DEFINITION 7. Suppose that X and Y are sets, and that f is a function from X into Y.
X is called the domain of f, and Y is called the codomain of f. The range of
f is the set {p : there is an element of f whose second coordinate is p.}

DEFINITION 8. Suppose that X and Y are sets and f is a function from X into Y.
The statement that f is one-to-one means that if (a,c) is an element of f
and (b,c) is an element of f, then a=b. The statement that f is injective
means that f is one-to-one.

DEFINITION 9. Suppose that X and Y are sets and f is a function from X into Y. The statement
that f is surjective means that the range of f is Y. The statement that f is a function from
X onto Y means that f is a surjective function from X into Y.

page revision: 6, last edited: 29 Mar 2010 11:29