Friday April 11

Proofs.
Proof by case check.
When the cases are "Q is true or Q is false", the proof gets abbreviated, and is called a proof by contradiction. Underneath, it's still really a case check.
Well-ordering axiom of the natural numbers.
Proving something for all natural numbers: if it's not true, then there's a least counterexample.
We saw one way of writing a "proof by induction", using a counterexample to produce a smaller counterexample.