Warm Up Order from least to greatest. 1. 10, –5, –10, 0, 5 2. 1. 10, –5, –10, 0, 5 2. –10, –5, 0, 5, 10

R Q Z W N Real Numbers Rational Numbers Ratios of integers, written in the form r=m/n, where m and n are integers and n≠0. The decimal form either terminates or repeats. Integers Natural numbers, their negatives, and zero. . . . , −3, −2, −1, 0, 1, 2, 3, . . . Whole Number Non-negative integers. 0, 1, 2, 3, . . . Natural numbers Counting numbers. 1, 2, 3, 4, . . . Irrational Numbers Cannot be written as a fraction. The decimal form is non-terminating and non-repeating. Q Z W N

Classifying Numbers

Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers

Set-Builder Notation Uses the properties of the elements in the set to define the set. Inequalities and the element symbol  are often used in the set-builder notation. The set of striped-billiard-ball numbers, or {9, 10, 11, 12, 13, 14, 15}, is represented in set-builder notation below: The set of all numbers x such that x has the given properties {x | 8 < x ≤ 15 and x  N} Read the above as “the set of all numbers x such that x is greater than 8 and less than or equal to 15 and x is a natural number.” The symbol  means “is an element of.” So x  N is read “x is an element of the set of natural numbers,” or “x is a natural number.” Helpful Hint

Roster Notation Lists each element of a set in braces. The set of striped-billiard-ball numbers is written {9, 10, 11, 12, 13, 14, 15}. This notation can be used for finite sets. Cannot use roster notation for infinite sets. Interval Notation Uses the symbols [and] to include endpoints and (and) to exclude endpoints from an interval.

Because ∞ and –∞ are not numbers, they cannot be included in a set of numbers, so parentheses are used to enclose them in an interval. The table shows the relationship among some methods of representing intervals.

Some representations of the same sets of real numbers are shown.

Is there a difference between saying that a real number is positive and saying that a real number is nonnegative?

Interval/Set Notation and Number Line Graphs

Express the interval in set notation and then graph.

Express the interval in set notation and then graph.

Express the interval in set notation and then graph.

Express the interval in set notation and then graph.

Express the interval in set notation and then graph.

Express the set in interval notation and then graph.

Express the set in interval notation and then graph.

Express the set in interval notation and then graph.

Express the set in interval notation and then graph.

Express the graph in set and interval notation.

Express the graph in set and interval notation.

Express the graph in set and interval notation.

Express the graph in set and interval notation.

Express the graph in set and interval notation.

Express the graph in set and interval notation.

Answers to Homework, page 10:

Review, Classifying Numbers Put in order from least to greatest, then classify:

Review, Roster, Set, and Interval Notation Most women have shoe sizes ranging in half sizes from 5 to 11. Represent this on a number lines and in roster notation.

Review, Roster, Set, and Interval Notation Children must be 5 to enter school and must leave once they turn 21. Represent this on a number line and using interval and set notation.