We've been proving stuff left and right. Now it's time to take a peek at what's going on under the hood. It's like we just learned to drive, and now we're about to get a crash course on how car engines work. Except our version will be way less greasy. Hopefully.
Proofs are all about logic, but there are different types of logic. Specifically, we're going to break down three different methods for proving stuff mathematically: deductive and inductive reasoning, and proof by contradiction.
Long story short, deductive proofs are all about using a general theory to prove something specific. Inductive proofs flip this around: we use a specific example to prove a general theory. Proofs by contradiction are their own weird thing: we prove something by showing that its opposite can't possibly be true.
Different strokes for different folks…er, different proofs, we mean.