# Elementary Set Theory, Part I

KAM-TIM LEUNG
DORIS LAI-CHUE CHEN
FOREWORD BY YUNG-CHOW WONG
Pages: 80
https://www.jstor.org/stable/j.ctt2jc4gs

1. Front Matter
(pp. i-ii)
(pp. iii-iv)
3. FOREWORD
(pp. v-vi)
Y. C. Wong

The most striking characteristic of modern mathematics is its greater unity and generality. In modern mathematics, the boundaries between different areas have become obscured; very often, what used to be separate and unrelated disciplines are now special cases of a single one; and, amid these far-reaching changes, there have emerged certain basic concepts, notations and terminologies that are of considerable importance and frequent use in a large portion of mathematics.

By 1959, I felt that the time was ripe for this University to introduce into its first-year mathematics course the most fundamental and the more elementary of these basic concepts,...

4. PREFACE
(pp. vii-viii)
K. T. Leung and Doris L. C. Chen
5. ### PART I

• CHAPTER 1 STATEMENT CALCULUS
(pp. 3-21)

By a statement (or a proposition or a declarative sentence) we understand a sentence of which it is meaningful to say that its content is true or false. Obviously, each of the following sentences is a statement:

Geography is a science.

Confucius was a soldier.

Cheung Sam is dead and Lee Sai is in prison.

2 is smaller than 3 and 3 is a prime number.

The steering gear was loose or the driver was drunk.

If John is here, then the book is not his.

Whereas none of the following sentences can be regarded as a statement in the...

• CHAPTER 2 SETS
(pp. 22-42)

A fundamental concept in mathematics is that of a set. This concept can be used as a foundation of all known mathematics. In this and the following chapters, we shall develop some of the basic properties of sets. In set theory, we shall be dealing with sets of objects. Here we take objects to be simply the individual things of our intuition and our thoughts. In what follows, objects are referred to by their names, usually letters. Thus in saying ‘an object is denoted by \$ x \$ ’ or ‘ \$ x \$ is an object’, we mean that ‘ \$ x \$ ’ is a name of the...

• CHAPTER 3 RELATIONS
(pp. 43-52)

We have seen in Section 2 E that, given any two objects \$ x \$ and \$ y \$ , there is a set \$ {x,y} \$ which has \$ x \$ and \$ y \$ as its only elements. Moreover, \$ {x,y} = {y,x} \$ ; in other words, the order in which the objects \$ x \$ and \$ y \$ appear is immaterial to the construction of the set \$ {x,y} \$ . For this reason the set \$ {x,y} \$ is called an unordered pair.

Let us recall a well-known technique used in plane analytic geometry. With respect to a fixed rectangular coordinate system, each point \$ P \$ in the plane is uniquely represented by a pair ( \$ x,y \$ ) of numbers...

• CHAPTER 4 MAPPINGS
(pp. 53-64)

Most readers are familiar with the graphical concept of functions. This involves in general a set \$ A \$ of objects called arguments, a set \$ B \$ of objects called values and an act of associating with each argument in \$ A \$ a unique value in \$ B \$ . In elementary calculus, an expression \$ y=f(x) \$ is used to represent an act of associating with each argument \$ x \$ (a real number) a unique value \$ y \$ (also a real number). Within the framework of set theory, this situation can be conveniently formulated by means of relations.

Definition 4.1. \$ A \$ mapping from (or of or on) a...

6. SPECIAL SYMBOLS AND ABBREVIATIONS
(pp. 65-66)
7. LIST OF AXIOMS
(pp. 66-66)
8. INDEX
(pp. 67-68)