Book of Proof

BOOK OF PROOF

(Second Edition)

Richard Hammack

Paperback: ISBN 978-0-9894721-0-4
Hardcover: ISBN 978-0-9894721-1-1

This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews.

The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) The two editions can be used interchangeably, except for the last few pages of Chapter 13. (But you can download them here.)

Order a copy from Amazon or Barnes & Noble for $15.65 or download a pdf for free here. Click here for a pdf copy of the entire book, or get the chapters individually below.

Note to adopters: Your bookstore will need to know that the book is distributed by Ingram. Please let me know if you use this book in your classes. I maintain a list of known adoptions here. Thanks!

Contents

(Click here for pdf contents, including sections of chapters.)
Preface

ix

Introduction
x
Part I: Fundamentals

1. Sets

3

2. Logic

33

3. Counting

63
Part II: How to Prove Conditional Statements

4. Direct Proof

87

5. Contrapositive Proof

102

6. Proof by Contradiction

111

Part III: More on Proof

	7. Proving Non-Conditional Statements	121
	8. Proofs Involving Sets	131
	9. Disproof	146
	10. Mathematical Induction	154

Part IV: Relations, Functions and Cardinality

11. Relations

175

12. Functions

196

13. Cardinality

217

Solutions
240

Index
301

Thanks to readers around the world who wrote to report mistakes and typos! I will continue to incorporate reader feedback in periodic revisions. Please contact me if you find any additional mistakes. My email address is on my home page.

© 2013 by Richard Hammack; This work is licensed under the Creative Commons Attribution-No Derivative Works 3.0 License
	ISBN: 978-0-9894721-0-4

	4. Direct Proof	87
	5. Contrapositive Proof	102
	6. Proof by Contradiction	111

	1. Sets	3
	2. Logic	33
	3. Counting	63

	11. Relations	175
	12. Functions	196
	13. Cardinality	217

Solutions	240
Index	301