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Transcript
1-1 Sets of Numbers Lesson Objective: Classify and order real numbers. Set - A collection of items Items in a set. Element - Subset - A set whose elements all belong to another set. Empty Set - Denoted by Ø, is a set containing no elements. Roster Notation - When the elements of a set are listed between braces, { }. Finite Set- Has a definite, or finite, number of elements. Infinite Set - Has an unlimited, or infinite, number of elements. Interval Notation – A method of describing an interval by specifying all number between two endpoints using the symbols [ and ] to include an endpoint and ( and ) to exclude the endpoint. Set-Builder Notation – A method of describing a set by using the properties of the elements of the set. Real Numbers Rational Numbers Integers Whole Numbers Natural Numbers Irrational Numbers WORDS NUMBER LINE INEQUALITY INTERVAL NOTATION Numbers less than 3 Numbers greater than or equal to -2 Numbers between 2 and 4 Numbers 1 through 3 WORDS All real numbers except 1 Positive odd Numbers Numbers within 3 units of 2 ROSTER INTERVAL SET-BUILDER NOTATION NOTATION NOTATION WORDS ROSTER NOTATION 1, 2, 3, 4, and 5 2 n 2 Whole numbers less than 3 INTERVAL NOTATION SET-BUILDER NOTATION -5 1. Consider the numbers .6, 2, 0, 2 , .5129 a. Order the numbers from least to greatest. b. Classify each number by the subset of real numbers to which it belongs. 2. Use the interval notation to represent each set of numbers a. b. 4x6 3. Translating between Methods of Set Notation Re-write each set in the indicated notation a. x x 2n and n ; words b. Numbers and symbols on a telephone keypad; roster notation c. ; set-builder notation