(N is studying calculus. She has just completed an induction proof of the power rule for negative exponents based on the quotient rule.)

N: Induction feels like cheating.

Me: I know, right?? You only prove 2 things, and then you’ve proved an infinite number of things.

N: It’s not just that, it’s that you already assume you’re right. It’s like you’re borrowing against your own rightness.