A proof of a mathematical statement is a logical argument which establishes the truth of the statement. The steps of the logical argument are provided by implications. One of the main aims of this book is to describe a variety of methods of proof so that you can follow these when you meet them and also construct proofs for yourself.
No doubt anyone reading this book will have been seeing and understanding proofs for years. At university you are expected to be able to construct your own proofs and, as importantly, to write them out carefully so that other people can understand them – or even so that you can understand them yourself when you come to look back at your. work some months later. One real difficulty is that we do not normally ...