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Published byClarissa Powers Modified over 5 years ago

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**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

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**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

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Classifying Numbers

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Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers

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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

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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.

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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.

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

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

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**Interval/Set Notation and Number Line Graphs**

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**Express the interval in set notation and then graph.**

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**Express the interval in set notation and then graph.**

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**Express the interval in set notation and then graph.**

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**Express the interval in set notation and then graph.**

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**Express the interval in set notation and then graph.**

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**Express the set in interval notation and then graph.**

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**Express the set in interval notation and then graph.**

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**Express the set in interval notation and then graph.**

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**Express the set in interval notation and then graph.**

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**Express the graph in set and interval notation.**

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**Express the graph in set and interval notation.**

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**Express the graph in set and interval notation.**

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**Express the graph in set and interval notation.**

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**Express the graph in set and interval notation.**

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**Express the graph in set and interval notation.**

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**Answers to Homework, page 10:**

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**Review, Classifying Numbers**

Put in order from least to greatest, then classify:

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**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.

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**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.

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