Choosing Your Weapon

Intro to Proofs · Axiom Academy

Every theorem has a proof technique that fits it best. Learn to read a statement and reach for the right one. There's no single best proof — only the best one for this theorem Direct proof, contrapositive, contradiction, proof by cases — these aren't four right answers and three wrong ones. They're tools, and each theorem has a shape that one of them fits cleanly. The skill isn't knowing the methods; it's matching the method to the statement in front of you. Watch one theorem get sized up against all four techniques at once. Each method's fit bar fills to how well it suits this statement — the awkward ones fade back, and the one that fits cleanly locks in as the weapon of choice. The theorem here — "there is no largest prime" — denies that something exists. Statements like that hand themselves to contradiction. Try it: read the theorem, reach for a weapon Pick a theorem, then choose the technique you'd attack it with. The best-fit method lights up green and the others dim — but try the "wrong" ones too: the verdict tells you why a method does or doesn't suit each statement. Pick a method above to see how well it fits this theorem. Notice the pattern: each theorem's wording is a hint. "No largest…" wants contradiction; "either/or" wants cases; an awkward conclusion wants the contrapositive. Several methods might work — one of them is elegant

This is the written version of the interactive lesson above. See the full Intro to Proofs course.