Chapter 3
Tackling a Longer Proof
IN THIS CHAPTER
Making a game plan
Starting at the start, working from the end, and meeting in the middle
Making sure your logic holds
Chapter 2 started you off with short proofs and a dozen and a half basic theorems. Here, I go through a single, longer proof in great detail, carefully analyzing each step. Throughout the chapter, I walk you through the entire thought process that goes into solving a proof, reviewing and expanding on the half dozen or so proof strategies from Chapter 2. When you’re working on a proof and you get stuck, this chapter is a good one to come back to for tips on how to get moving again. The proof I’ve created for this chapter isn’t so terribly gnarly; it’s just a bit longer than the ones in Chapter 2. Here it is:
Making a Game Plan
A good way to begin any proof is to make a game plan, or rough outline, of how you’d do the proof. A game plan is your common sense argument of how you’d get from the given facts to the ...
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