Page 17 - Algebra 1

L E1S S O N Classifying Real Numbers
Warm Up
Start off each lesson by practicing prerequisite skills and math vocabulary that will make you more successful with today’s new concept.
1. Vocabulary A (Venn diagram, line plot) shows the relationship
(SB 30)
Write each fraction as a decimal. 2. _2
(SB5) 9
between sets.
Write each decimal as a fraction in simplest form.
4. 0.6 5. 5.75 (SB 6) (SB 6)
3. 4_3 (SB5) 8
New Concepts
A set is a collection of objects. Each object in the set is called an element.
A set is written by enclosing the elements within braces. There are three types of sets. A set with no elements is called the null or empty set. A set with a finite number of elements is a finite set. An infinite set has an infinite number of elements.
{12, 24, 36} {1, 3, 5,...} finite set infinite set
The subsets of real numbers are infinite sets.
{ } or ∅ null or empty set
Subsets of Real Numbers
Natural Numbers
The numbers used to count objects or things. {1, 2, 3, 4,...}
Whole Numbers
The set of natural numbers and zero. {0, 1, 2, 3, 4,...}
Integers
The set of whole numbers and the opposites of the natural numbers.
{..., -4, -3, -2, -1, 0, 1, 2, 3, 4,...}
Rational Numbers
Numbers that can be written in the form _a , where b
a and b are integers and b ≠ 0. In decimal form, rational numbers either terminate or repeat.
Examples: _1 , 0.−3, - _2 , 0.125 23
Irrational Numbers
Numbers that cannot be written as the quotient of two integers. In decimal form, irrational numbers neither terminate nor repeat.
Examples: √3 5 , √ 2, -√ 2, 3√3 , π, 3π
Real Numbers The set including all rational and irrational numbers.
Reading Math
The three dots inside the braces are called an ellipsis. An ellipsis shows that the numbers in the set continue on without end.
Online Connection www.SaxonMathResources.com
2 Saxon Algebra 1