Proofs

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
• Proof by induction
  • Loop invariant
  • Substitution method
• Epsilon-delta definition
• Proof by counterexample
  • To show that the general statement does not hold for all cases.

See also

• Axiom
• Theorem