1. Ch1.2_RealNumbers.notebook August 23, 2011
WARM­UP
Write at least four subsets of the following set
A = { a, b, c, d}
Find the solution set for
the following open sentence
X2 = 25
Aug 21­9:12 AM
Chapter 1.2
Real Numbers
Aug 21­9:10 AM
1

2. Ch1.2_RealNumbers.notebook August 23, 2011
The Set of Natural Numbers
Counting numbers
{ 1, 2, 3, 4, ... }
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
The Set of Whole Numbers
Counting numbers and zero
{ 0, 1, 2, 3, 4, ... }
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
2

3. Ch1.2_RealNumbers.notebook August 23, 2011
The Set of Integers
Whole numbers and
their opposites (negatives)
{ ..., ­2, ­1, 0, 1, 2, 3, ... }
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
The Set of Rational Numbers
Numbers that can be expressed
as a ratio of two integers
­ 4 5 1
{ , ­3 , 0, , 2.67, }
2 4
1
Ratios lie between integers
on a number line
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
3

4. Ch1.2_RealNumbers.notebook August 23, 2011
Irrational Numbers
Numbers that can not be expressed
as a ratio of two integers
Examples
π , √2
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
Real Numbers
All rational and irrational numbers
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:17 AM
4

5. Ch1.2_RealNumbers.notebook August 23, 2011
In General
Real numbers
Rational numbers
Irrational numbers
Integers
Whole numbers
Natural numbers
Aug 21­9:36 AM
Symbols
< Less than
≤ Less than or equal to
> Greater than
≥ Greater than or equal to
= Equal
≠ Not equal
Aug 21­9:34 AM
5

6. Ch1.2_RealNumbers.notebook August 23, 2011
Absolute Value | |
The distance from zero on a number line
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10
­7 is 7 spaces from zero
So |­7| = 7
Aug 21­10:08 AM
Example
What set of numbers is represented on the
number line?
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:51 AM
6

7. Ch1.2_RealNumbers.notebook August 23, 2011
Example
Graph the set of real numbers on
the number line
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
Aug 21­9:51 AM
Example
Fill in the blanks with
the correct inequality sign
­3 ____ 5
.75 ___ ­ | ­4 |
Aug 21­9:54 AM
7

8. Ch1.2_RealNumbers.notebook August 23, 2011
Example
Use the following information
to write an inequality
Jimmy spent $4.23 at Taco Bell
Suzie spent $3.19 at Taco Bell
Aug 21­9:54 AM
Page 13
1 ­ 34
Aug 21­10:06 AM
8

9. Ch1.2_RealNumbers.notebook August 23, 2011
Aug 22­8:22 AM
9