DeVry University Mathematics Bridge Program: Algebra
Mathematics Bridge Program ©2002 DeVry University
Algebra
Chapter 1
The Real Number System
1.1. The Number Sets
• Natural Numbers • Whole Numbers • Integers • Rational Numbers • Irrational Numbers • Real Numbers
1.2. Operations With Real Numbers • Absolute Value • Addition • Subtraction • Multiplication • Division • Order of Operations
1.3. Answers to Exercises
1.1 The Number Sets
A set is a collection of objects. The objects in a set are called the elements of the set. A set of numbers is simply a listing, within braces {}. For example, the set of numbers used for counting can be represented as S = {1, 2, 3, 4, 5, . . .}. The braces
{ } indicate that we are representing a set.
Some important sets of numbers that we will study are the following:
Natural numbers: The natural numbers N are the counting numbers. N= {1, 2, 3, 4, . . .}.
Whole numbers: The whole numbers W are the natural numbers combined with the number 0. W = {0, 1, 2, 3, 4, . . .}.
Integers: The integers I are the whole numbers combined with the negative of all natural numbers. I = { . . ., -4, -3, -2, -1, 0, 1, 2, 3, 4, . . .}. Z can also be used to represent the integers.
The integers consist of the following numbers: • Positive integers: {1, 2, 3, 4, . . .} • Negative integers: { . . . -4, -3, -2, -1}. (negative bank balance) • Zero is also an integer but it is neither positive nor negative.
Rational numbers: Q represents the rational numbers. A rational number is any number in the form [pic], where a and b are integers and b [pic]0. For example, [pic]. Note that all integers are also rational numbers, since any integer can also be expressed in the form [pic]
Example 1: Show that 3 is
Algebra
Chapter 1
The Real Number System
1.1. The Number Sets
• Natural Numbers • Whole Numbers • Integers • Rational Numbers • Irrational Numbers • Real Numbers
1.2. Operations With Real Numbers • Absolute Value • Addition • Subtraction • Multiplication • Division • Order of Operations
1.3. Answers to Exercises
1.1 The Number Sets
A set is a collection of objects. The objects in a set are called the elements of the set. A set of numbers is simply a listing, within braces {}. For example, the set of numbers used for counting can be represented as S = {1, 2, 3, 4, 5, . . .}. The braces
{ } indicate that we are representing a set.
Some important sets of numbers that we will study are the following:
Natural numbers: The natural numbers N are the counting numbers. N= {1, 2, 3, 4, . . .}.
Whole numbers: The whole numbers W are the natural numbers combined with the number 0. W = {0, 1, 2, 3, 4, . . .}.
Integers: The integers I are the whole numbers combined with the negative of all natural numbers. I = { . . ., -4, -3, -2, -1, 0, 1, 2, 3, 4, . . .}. Z can also be used to represent the integers.
The integers consist of the following numbers: • Positive integers: {1, 2, 3, 4, . . .} • Negative integers: { . . . -4, -3, -2, -1}. (negative bank balance) • Zero is also an integer but it is neither positive nor negative.
Rational numbers: Q represents the rational numbers. A rational number is any number in the form [pic], where a and b are integers and b [pic]0. For example, [pic]. Note that all integers are also rational numbers, since any integer can also be expressed in the form [pic]
Example 1: Show that 3 is