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§ 1.2 Symbols and Sets of Numbers Set of Numbers • Natural numbers – {1, 2, 3, 4, 5, 6 . . .} • Whole numbers – {0, 1, 2, 3, 4 . . .} • Integers – {. . . –3, -2, -1, 0, 1, 2, 3 . . .} • Rational numbers – the set of all numbers that can be expressed as a quotient of integers, with denominator 0 • Irrational numbers – the set of all numbers that can NOT be expressed as a quotient of integers • Real numbers – the set of all rational and irrational numbers combined Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Equality and Inequality Symbols Symbol a=b ab a<b a>b ab ab Meaning a is equal to b. a is not equal to b. a is less than b. a is greater than b. a is less then or equal to b. a is greater than or equal to b. Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 The Number Line A number line is a line on which each point is associated with a number. –5 –4 –3 –2 –1 – 4.8 Negative numbers 0 1 2 3 4 5 1.5 Positive numbers Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 Order Property for Real Numbers For any two real numbers a and b, a is less than b if a is to the left of b on the number line. • a < b means a is to the left of b on a number line. • a > b means a is to the right of b on a number line. Example Insert < or > between the following pair of numbers to make a true statement. 7 0 8 Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 Absolute Value The absolute value of a real number a, denoted by |a|, is the distance between a and 0 on the number line. | – 4| = 4 Symbol for absolute value |5| = 5 Distance of 4 –5 –4 –3 –2 –1 Distance of 5 0 1 2 3 4 5 Martin-Gay, Beginning and Intermediate Algebra, 4ed 6