CHAPTER 3: THE INTEGERS Z
MATH 378, CSUSM. SPRING 2009. AITKEN
1. Introduction The natural numbers are designed for measuring the size of finite sets, but what if you want to compare the sizes of two sets? For example, you might want to compare the number
CHAPTER 2: EXPLORING N
MATH 378, CSUSM. SPRING 2009. AITKEN
1. Introduction In this chapter we continue the study of the set N. We begin with subtraction n m where we assume n m. Then we consider the well-ordering property of N and the related maximum pri
CHAPTER 6: RATIONAL NUMBERS AND ORDERED FIELDS
LECTURE NOTES FOR MATH 378 (CSUSM, SPRING 2009). WAYNE AITKEN
1. Introduction In this chapter we construct the set of rational numbers Q using equivalence classes of pairs of elements of Z. Informally, the co
CHAPTER 1: THE PEANO AXIOMS
MATH 378, CSUSM. SPRING 2009. AITKEN
1. Introduction We begin our exploration of number systems with the most basic number system: the natural numbers N. Informally, natural numbers are just the ordinary whole numbers 0, 1, 2,
CHAPTER 0: BACKGROUND (SPRING 2009 DRAFT)
MATH 378, CSUSM. SPRING 2009. AITKEN
This chapter reviews some of the background concepts needed for Math 378. This chapter is new to the course (added Spring 2009), and is still in rough form. It may be extended
CHAPTER 9: COMPLEX NUMBERS
LECTURE NOTES FOR MATH 378 (CSUSM, SPRING 2009). WAYNE AITKEN
1. Introduction Although R is a complete ordered field, mathematicians do not stop at real numbers. The real numbers are limited in various ways. For example, not eve
CHAPTER 8: EXPLORING R
LECTURE NOTES FOR MATH 378 (CSUSM, SPRING 2009). WAYNE AITKEN
In the previous chapter we discussed the need for a complete ordered eld. The eld Q is not complete, so we constructed the real numbers R. In this chapter we investigate
CHAPTER 7: REAL NUMBERS
LECTURE NOTES FOR MATH 378 (CSUSM, SPRING 2009). WAYNE AITKEN
1. Introduction In this chapter we construct the set of real numbers R. There are several ways to introduce the real numbers. Three popular approaches are to introduce R