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Elementary Set Theory, Part I

K.T. Leung ,Doris Lai-chue Chen

Publication Year: 1992

This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

Published by: Hong Kong University Press, HKU

Title Page, Copyright

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CONTENTS

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pp. iii-

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FOREWORD

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pp. v-vi

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 ...

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PREFACE

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pp. vii-viii

Elementary Set Theory is an extension of the lecture notes for the course 'Fundamental Concepts of Mathematics* given each year to first-year undergraduate students of mathematics in the University of Hong Kong since 1959. The purpose of this course, arranged in about twenty-five lectures, is to provide students of mathematics with the ...

PART I

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pp. 1-2

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CHAPTER 1. STATEMENT CALCULUS

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pp. 3-21

Throughout this chapter, we shall mainly be concerned with statements. Here we shall briefly describe what we propose to do with them. In the statement calculus (or propositional calculus) of this chapter, with the exception of Sections K and L, we shall not concern ourselves with the relation between the subjects and the predicates of the statements. ...

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CHAPTER 2. SETS

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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. ...

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CHAPTER 3. RELATIONS

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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. ...

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CHAPTER 4. MAPPINGS

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pp. 64-75

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 ...

SPECIAL SYMBOLS AND ABBREVIATIONS/ List of Axioms

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pp. 65-66

INDEX

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pp. 67-68


E-ISBN-13: 9789882201187
Print-ISBN-13: 9789622090132

Page Count: 80
Publication Year: 1992