Guides ยท Math
Proof Techniques Basics
Learn core proof patterns
This guide introduces common proof techniques and how to choose among them: direct proof for constructive arguments, contrapositive/contradiction for logical structure, and induction for statements over integers.
- proofs
- induction
- contradiction
- contrapositive
- logic
Direct proof
Start from assumptions and apply definitions/known results step-by-step until the conclusion follows.
Contrapositive and contradiction
Rewrite implications or assume the opposite to expose a logical conflict.
Induction
Prove a base case, assume n, then show n+1; be explicit about the inductive hypothesis.
Write cleanly
State assumptions, define symbols, and end with a clear conclusion so the argument is easy to follow.