LOGIC SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

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.