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1.1 B Sets and Real Numbers February 07, 2011 MATH 1010 ~ Intermediate Algebra Chapter 1 Fundamentals of Algebra Section 1.1: Sets and Real Numbers Objectives: ❖ ❖ ❖ ❖ Understand the set of real numbers and the subsets of real numbers. Order numbers on the real number line. Determine the distance between two numbers on the real number line. Determine the absolute value of a real number. | 0 | 1 -2 3 5 ∛8 √2 7 3 0 π 1.1 B Sets and Real Numbers The Real Number System Natural numbers Whole numbers Integers Rational numbers Irrational numbers Real numbers ≈ means approximately equal to. February 07, 2011 1.1 B Sets and Real Numbers February 07, 2011 ①Example: To which set(s) do each of these numbers belong? 3 5 -2 ∛8 π √2 0 7 3 a. Natural b. Whole c. Integers d. Rational e. Irrational ② Example: Put each of the numbers above on this number line. | 0 a< b means: a > b means: | 1 1.1 B Sets and Real Numbers February 07, 2011 The distance between two points: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 1.1 B Sets and Real Numbers February 07, 2011 The opposite of a number: 0 1.1 B Sets and Real Numbers February 07, 2011 The absolute value of a number: |a| = a if a≥0 |a| = -a if a<0 0 ③ Example: a) b) c) d) |-5| = |5| = |5| = - |5| = ④ Example: Find the opposite of each number and the absolute value of each number. a) -32 b) 17