This document provides an overview of different sets of real numbers including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. It defines each set and provides examples. Graphs and number lines are used to illustrate the different sets. Examples are given to practice identifying sets of numbers from graphs, filling in inequality signs, and writing inequalities based on numeric comparisons.

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
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Chapter 1.2
Real Numbers
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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
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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
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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
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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
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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
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Real Numbers
All rational and irrational numbers
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5. Ch1.2_RealNumbers.notebook August 23, 2011
In General
Real numbers
Rational numbers
Irrational numbers
Integers
Whole numbers
Natural numbers
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Symbols
< Less than
≤ Less than or equal to
> Greater than
≥ Greater than or equal to
= Equal
≠ Not equal
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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
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Example
What set of numbers is represented on the
number line?
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
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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
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Example
Fill in the blanks with
the correct inequality sign
­3 ____ 5
.75 ___ ­ | ­4 |
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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
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1 ­ 34
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9. Ch1.2_RealNumbers.notebook August 23, 2011
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