# Logic, Sets and the Techniques of Mathematical Proofs: A Companion for High School and College Students

AuthorHouse, 2011 - 356 pàgines
As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

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### Continguts

 Preface 11 Chapter 1 Propositional logic 17 Chapter 2 Tautologies and contradictions 37 Chapter 3 Theorems and Proof methods 49 Chapter 4 Sets 62 Chapter 5 Operations on sets 81 Chapter 6 Singlevariable sentential logic 101 Chapter 7 Sentential implications and equivalences 115
 Chapter 12 Methods of proof by mathematical induction 203 Chapter 13 Relations 218 Chapter 14 Functions and absolute value 239 Chapter 15 types of functions 254 Chapter 16 Sequences 273 Chapter 17 Fundamental and monotonic sequences 295 Chapter 18 Finite and Infinite sets 309 Chapter 19 Indexed Family of sets 328

 Chapter 8 Twovariable predicate logic 125 Chapter 9 Real numbers 139 Subtraction and Division 160 The axiom of continuity 176
 Bibliography 348 Index of Mathematical Terms 349 Copyright