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 injectivemeans 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.