ABSTRACT
This chapter begins with some simple examples of proofs to illustrate the basic principles and explores how to prove statements. Lists of statements or equations with little or no words connecting them will instead be considered a sketch of a proof and not a proof itself. Proofs are written in proper English. Correct grammar is necessary. Further, there should be a flow from sentence to sentence that carries the reader through the argument. An analogy can be made comparing a painter to a proof writer. In addition, emphasis is placed on how to write proofs. The chapter explains how to write proofs based on the Principle of Generalization. For some statements, a direct approach to a proof is not the best, or may not even be feasible. The chapter presents some alternatives for proof writing. It considers some proofs of facts about the real numbers and real functions.
