1.2.1 Proof by Contradiction
PROFESSOR: It's doubtful if you really understand something if you can explain why it's true. That's what proofs are about in mathematics and in computer science. So we're going to be talking about proofs of lots of things that we're trying to understand. And in particular, we're going to look at a proof technique now called proof by contradiction, which is probably so familiar that you never noticed you were using it. And now we're going to call explicit attention to it, and think about it. So let's do an example first to see what's going on. Suppose that I wanted to prove that the cube root of 1,332 was less than or equal to 11. Or more precisely, suppose I didn't know and I'm asking this question, is the cube root of 1,332 less than or equal to 11? Well, one way to do it would be to simply compute the cube root of 1,332, which is a small bother, but manageable. But there's a simpler way than figuring out how to compute a ...