Mathematical Modeling in the Social and Life Sciences

APPENDIX I

Sets

By a set we mean a well-defined collection of objects, called the elements or (members) of the set. Some examples of sets are

1. The set A of real numbers less than 21

2. The set B of college sophomores in Texas universities

3. The set C of negative integers

4. The set D of three-headed residents of Muskegon, Michigan

5. The set E of solutions of the equation tan x − log x = x³

6. The set F of integers strictly between 3 and 10

We use the notation “x ∈ X” to represent the statement that “The element x is a member of the set X.” If x is not an element of X, denote this by x ∉ X. In our examples, 4 ∈ A and 24 ∉ A.

Sets may be described in terms of some common property shared by the elements. A set may also be given by listing all its members; when this is done, the elements are typically written within braces. Here are some further examples:

7. G = {single, double, triple, home run}

8. H = {4, 5, 6, 7, 8, 9}

9. I = { 1,2, 3, ...}

10. J = {Washington, Adams, Jefferson, ..., Clinton, Bush, Obama}

Some sets occur so frequently in applications that special symbols have been invented for them. The set of real numbers, for example, is commonly denoted by and the set of integers by .

A third way of describing a set is by a special notation easily understood by an example. ...