E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals A1 E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals The Real Numbers System KFUPM - Prep Year Math Program (c) 2009 All Right Reserved  Set of Numbers  Ordering of Real Numbers  Absolute Value  Interval of Real

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Set of Numbers Natural Numbers The set of natural numbers (counting numbers) is {1, 2, 3, 4, 5...} Whole Numbers The set of whole numbers (including 0 with the set of natural numbers) is {0, 1, 2, 3, 4, 5...} Integers Integers are the expanded set of numbers obtained by including the negative of the counting numbers. {... –4, –3, –2, –1, 0, 1, 2, 3, 4...} KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Set of Numbers Rational Numbers Rational numbers are set of all numbers of the form where a (called numerator) and b (called denominator) are integers. Irrational Numbers Irrational numbers are real numbers that are not rational. Equivalently, they are non-terminating and non-repeating decimals. For example KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Set of Numbers The Real Numbers The set of all the irrational numbers and the rational numbers constitutes the set of the real numbers. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Irrational numbers 1 − π − e e e − π Rational numbers Integers -1, -2, -3, - 4,.… Whole number 0 Natural numbers 1, 2, 3, ….

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Ordering of Real Numbers The real number system has the property of being ordered. This means that for any two different real numbers a and b, one and only one of the following three statements must be true: a b. This property allows the arrangement of the real numbers on any line, L, as shown in the figure below. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Absolute Value The absolute value of a real number is the distance from the number to the origin O on the number line. The absolute value of x is denoted by │x│. Absolute Value Properties Definition: We define the distance between two numbers a and b by │a − b│ KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Intervals of Real Numbers KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) because b). because c). because d). because e). because f). because KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 1 Use the definition of the absolute value to evaluate

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) because b) because c). because d).. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 2 For 0<x<1, simplify each absolute value expression. because

E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 3 Use the absolute value to describe each statement. a) the distance between k and 4 is 2 b) the distance between x and –3 is less than 1 c) the city of Jeddah is closer to Makkah than it is to Madinah d)the city of Hail is more than 100 kilometers away from Buraidah