Fundamentals of Supply Chain Theory, 2nd Edition

Appendix B How to Write Proofs: A Short Guide

B.1 How to Prove Anything

OK, fine—we can't actually tell you how to prove everything. But we can give you some advice that will help you when you try to prove anything.

Writing a proof is more art than science. Although there may be a “correct” way to prove something (or several correct ways), there is still a wide range of styles, formats, and logical implications that follow the same basic argument. (Similarly, you and your friend might write very different essays on “How I Spent My Summer Vacation,” even if you did the same things during your vacations.)

Writing a proof is very much like arguing a case in court. (Or at least it's like how it looks on TV.) Like a courtroom argument, a proof should contain a beginning, a middle, and an end.

• The beginning tells us what is already known (the assumptions of the theorem), reminds us of important facts that are already in evidence that will be important for the proof, establishes new notation that you will use in the proof, and gives us a hint of where you're headed and what steps the proof will take. Here are some examples:

  Courtroom Claim: Dr. Evil is guilty of stealing pencils from Prof. Plum's desk.

  Courtroom Argument: Consider the man sitting before you, Dr. Evil. You already know that security camera video from the night of October 6 shows Dr. Evil entering Prof. Plum's office building. Let the security video tape from that night be labeled as “Exhibit A.” Today I will ...