初探归纳证明

Proof by Induction

Concept

Mathematical induction works the same way as dominoes: if we set them all up, and then knock over just the first one, they will all fall down. Induction works for any proof in which we need to prove an infinite number of cases (actually, it must be a countably infinite number of cases—you’ll understand what this means in Chapter $8$).

Let’s say we’re able to set up the dominoes by proving the following: