Math basics › Proofs
Writing a proof
Unpack the definitions
Write down what you know and what you want. “n is even” means n = 2k for some integer k, and most proofs start by unpacking a word like that.
Direct proof
Assume the “if” part and work forward until you reach the “then” part.
Contrapositive and contradiction
“If P then Q” is the same as “if not Q then not P”, which is sometimes easier. Contradiction: assume the opposite and reach something impossible.
To disprove one
One counterexample is enough. But examples never prove a statement for every n.