Section 1.1 Real Numbers and Their Graphs

ALGEBRA II. NOTES SECTION 1.1 REAL NUMBERS AND THEIR GRAPHS

What is a set?

Give me an example of a set:

For this section, we will be looking at sets of numbers. DEFINITIONS: 1.) Set – collection of numbers that satisfy a specific condition. Denoted by braces { }. Examples: a.) Natural (Counting) Numbers – denoted by - {1,2,3,...} b.) Whole Numbers – 0 + the set of - {0,1,2,3,...} c.) Integers – denoted by - consists of positive and negative integers and zero. {..., 2,  1,0,1,2,...} d.) Rational Numbers – denoted by - numbers that can be represented as a quotient where one integer is divided by a nonzero integer. 5 1 3 100 Examples: , , , 7 2 1 25 e.) Irrational Numbers – numbers that are not rational. Examples:  2, 3, f.) Real Numbers – denoted by - the set consisting of all rational and irrational numbers. g.) Venn Diagram – a geometric representation of the relationships indicated. Draw a Venn Diagram illustrating the sets of numbers defined above:

h.) Number Line – shows the order of numbers.

Origin Negative #’s Positive #’s -4 -3 -2 -1 0 1 2 3 4

Rules about Number Lines: 1.) Graph of 0 is the origin. 2.) Each point on a # line is paired with exactly 1 real # - Coordinate of the point. 3.) Each real # is paired with exactly 1 point on the line – Graph of a #. 4.) The # line is increasing from left to right. 3  1and 1   3 5.) Distance between the graph of a # and the origin is called Absolute Value – denoted by - always positive or 0. Note: distance can never be negative. Examples: 3  0  2 12 

Def.: Absolute Value – For any real # x, xmax{ x ,  x } . 6.) Opposite Numbers – numbers that have the same absolute value.

7.) Distance between 2 points on a number line = how many units they are away from each other. Ex. Find the distance from A to B. A B

-4 -3 -2 -1 0 1 2 3 4 5 6

Rule: d x1  x 2

Sample Problems: pgs. 4-5 8.)