ABSTRACT

The concept of proof is fundamental to all of mathematics. It is not enough to simply demonstrate with an example that a certain general result holds. This chapter investigates different types of proof techniques. There is another word in the definition of proof that will be stressed: “process.” Processes have certain rules that they must follow, yet there is oftentimes room for personalization. Each step of the process follows logically from axioms, stated assumptions or previously established results until the desired mathematical result is reached. Different mathematicians may choose to use alternative symbols or methods to accomplish the same goals that Proof and do. Some will indent an entire proof, much like a lengthy quotation in expository writing. The open square signifying the end of the proof may be replaced with.