Intermediate Algebra (11th edition)

FIGURE 5shows the set of real numbers. Every real number is either rational or ir-

rational. Notice that the integers are elements of the set of rational numbers and that

the whole numbers and natural numbers are elements of the set of integers.

SECTION 1.1 Basic Concepts 5

Sets of Numbers

Natural numbers, or

counting numbers

Whole numbers

Integers

Rational numbers

Examples: or 4, 1.3, or or 2, or 3,

Irrational numbers

Examples:

Real numbers 5 xx is a rational number or an irrational number 6 *

 3 , - 2 , p

5 xx is a real number that is not rational 6

14 - 29 -^4 12 ,^168 ^9 0.6

E

p

q^  p and q are integers, q^0 F

5 Á , 3, 2, 1, 0, 1, 2, 3, Á 6

5 0, 1, 2, 3, 4, 5, 6, Á 6

5 1, 2, 3, 4, 5, 6, Á 6

NOW TRY
EXERCISE 3
List the numbers in the
following set that are ele-
ments of each set.

(a)Whole numbers

(b)Rational numbers

 5 , p, 5F

E-2.4, - 1 , -^12 , 0, 0.3,

OBJECTIVE 3 Know the common sets of numbers.

(a)Integers

- 8,0, and 2

(b)Rational numbers

0, 0.5, 1.12,and 2

1

- 3 ,

9

- 8, 64 ,

(c) Irrational numbers

-  5 , , and  3 p NOW TRY

(d)Real numbers

All are real numbers.

Identifying Examples of Number Sets

List the numbers in the following set that are elements of each set.

e-8, - 5 , -

9

64

, 0, 0.5,

1

3

, 1.12,  3 , 2, pf

EXAMPLE 3

Rational numbers

Real numbers

Irrational numbers

Integers

..., –3, –2, – 1

Whole

numbers

Natural

numbers

0

1, 2, 3,...

• 8
  15
  23

4

4

π

π

4

-^1
5
–3^2

• 0.125 1.5 0.18

9

4

7

11

FIGURE 5

*An example of a number that is not real is. This number, part of the complex number system, is

discussed in Chapter 8.

- 1

NOW TRY ANSWERS

3. (a)

(b)E-2.4, - 1 , -^12 , 0, 0.3, 5F

5 0, 5 6