§ 1.2 Symbols and Sets of Numbers

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 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 33 Equality and Inequality Symbols SymbolMeaning a = b a  b a < b a > b a  b a  b 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 44 The Number Line A number line is a line on which each point is associated with a number. 2– – 1– 3– 4– 5 Negative numbers Positive numbers –

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 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. Order Property for Real Numbers Insert between the following pair of numbers to make a true statement. Example

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 Absolute Value The absolute value of a real number a, denoted by |a|, is the distance between a and 0 on the number line. 2– – 1– 3– 4– 5 | – 4| = 4 Distance of 4 Symbol for absolute value |5| = 5 Distance of 5