1.1.1 Sets of Numbers
Key Objectives • Order and classify real numbers. • Use interval notation to represent a set of numbers. • Translate between methods of set notation. Key Terms • A set is a collection of items called elements .
• Interval notation is a way of writing the set of all real numbers between two endpoints. The symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval. • Set-builder notation is a notation for a set that uses a rule to describe the properties of the elements of the set. • Roster notation is a way of representing a set by listing the elements between braces, { }. Example 1 Ordering and Classifying Real Numbers Rational numbers can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal form of a rational number either terminates, such as 1/2 = 0.5, or repeats, such as − 1/11 = − 0.090909... = 0.09. Irrational numbers, such as 2 and π , cannot be expressed as a quotient of two integers, and their decimal forms do not terminate or repeat. However, the value of these numbers can be approximated using terminating decimals. Real numbers in their decimal forms can be easily compared, as demonstrated by Prof. Burger in the following example.
9
Made with FlippingBook flipbook maker