In mathematics, a proof is a logical set of statements or calculations that validates the truth of a general statement beyond any doubt. Proofs are a major driver of rigour in mathematics, and thus are important (but not for engineers).
We have a few useful methods to prove statements. Our most common types are:
- Direct proof
- Contrapositive proof
- Proof by contradiction
- Induction
- Epsilon-delta definition
- Proof by counterexample
- To show that the general statement does not hold for all cases.