Proof
Mathematical proof is a rigorous argument that establishes the truth of a statement beyond any doubt. Learning to read and write proofs is central to all advanced mathematics.Key Topics
- Direct Proof — assuming premises and deriving the conclusion step by step
- Proof by Contradiction — assuming the negation and reaching a contradiction
- Proof by Contrapositive — proving the contrapositive of an implication
- Mathematical Induction — base case + inductive step for statements over natural numbers
- Strong Induction — using all preceding cases in the inductive step
- Proof by Cases — exhaustively covering all possibilities
- Existence & Uniqueness Proofs — constructive and non-constructive approaches
- Diagonalization — Cantor’s technique for uncountability and beyond