Proof Techniques

readme.md

Proof Techniques

There are only about 10-12 general proof techniques you need to consider, with only 2 or 3 being most common.

Proof by Logical Transformation

This can prove the conclusion by combining chains/trees of axioms, definitions, and earlier theorems.

Proof by Mathematical Induction

This is the second most common proof technique.

Proving correctness of algorithms via loop invariants is induction.

Proof by Contraposition

Proof by Contradiction

Proof by Example

Also called proof by construction.

Proved by constructing an explicit example. It can also be used to construct a counterexample to disprove a proposition that all elements have a certain property.

Proof by Exhaustion

The shortest known proof of the four color theorem as of 2011 still has over 600 cases.

Probabilistic proof

Combinatorial proof

Nonconstructive proof