All Modules

Proof Techniques

Master mathematical proof through 18 interactive demonstrations.

See also: Logic for the formal validity behind every accepted argument, Set Theory for structural induction and well-founded recursion, and Real Analysis for the rigorous epsilon-delta proofs that define the field.

  1. 01

    Direct Proof

    Prove P → Q by assuming P and logically deriving Q step by step

    3 demos
  2. 02

    The Pigeonhole Principle

    If n+1 pigeons fly into n holes, at least one hole has 2+ pigeons

    3 demos
  3. 03

    Mathematical Induction

    Prove infinite statements using the domino effect

    3 demos
  4. 04

    Well-Ordering Principle

    Every non-empty set of positive integers has a smallest element

    3 demos
  5. 05

    Proof by Contradiction

    Prove statements by showing their negation leads to impossibility

    3 demos
  6. 06

    Proof by Contrapositive

    Prove P → Q by proving the equivalent ¬Q → ¬P

    3 demos

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