100 Per Cent Mathematics Proof

Proof has been, and remains, one of the concepts which characterizes mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, this text seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principal techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, and constructive and non-constructive proofs. Many examples of proofs are presented and some common student errors are explained. The exercises assume only a secondary school background in mathematics, although examples from analysis and modern algebra are included.