The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers

Front Cover
In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above, it will be of most use to university or college students who are taking, or who have taken, an introductory course in analysis. Such a course will not automatically cover all the material dealt with in this book and so particular care has been taken to present the material in a manner which makes it suitable for self-study. In a particular, there are a large number of examples and exercises and, where necessary, hints to the solutions are provided. This style of presentation, of course, will also make the book useful for those studying the subject independently of taught course.
 

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Contents

Introduction page
1
Set operations
21
Relations
28
Functions
33
Real numbers
44
Principle of induction
54
Real numbers II
62
10+ Construction of the number systems
78
3+ Natural numbers
79
20+ Complex numbers
92
20+ Radicals
107
20+ Transcendental numbers
121
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