Section 1.2 Introduction to Algebra and the Set of Real Numbers 27 Table 1-1 summarizes the relational operators that compare two real numbers a and b. Table 1-1 Mathematical Expression Translation Example a 6 b 2 6 3 a is less than b. a is greater than b. a is less than or equal to b. a is greater than or equal to b. a is equal to b. a is not equal to b. a 7 b 5 7 1 a b 4 4 a b 10 9 a b 6 6 a b 7 0 a b a is approximately equal to b. 2.3 2 6, 7, , , The symbols and are called inequality signs, and the statements and are called inequalities. a 6 b, a 7 b, a b, a b, a b Ordering Real Numbers Example 6 The average temperatures (in degrees Celsius) for selected cities in the United States and Canada in January are shown in Table 1-2. Table 1-2 City Temp (C) Prince George, British Columbia 12.5 Corpus Christi,Texas 13.4 Parkersburg,West Virginia 0.9 San Jose, California 9.7 Juneau, Alaska 5.7 New Bedford, Massachusetts 0.2 Durham, North Carolina 4.2 Plot a point on the real number line representing the temperature of each city. Compare the temperatures between the following cities, and fill in the blank with the appropriate inequality sign: 6 or 7. Solution: a. Temperature of San Jose temperature of Corpus Christi b. Temperature of Juneau temperature of Prince George c. Temperature of Parkersburg temperature of New Bedford d. Temperature of Parkersburg temperature of Prince George Prince George Juneau Parkersburg New Bedford Durham San Jose Corpus Christi 15 10 5 0 5 10 15
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