Methods of Proof · 16 lessons

A proof is an argument that covers every case at once, including the cases nobody will ever check. Checking a thousand cases is evidence. A proof settles the question. The methods in this topic are the shapes that argument can take.

1. 1Proof by Induction: Summing 1 to n
2. 2Proof by Induction: Divisibility
3. Patterns and page numbers (11)
4. Sequences and Series (10)
5. 3Matrix Powers by Induction
6. Matrix Arithmetic (10)
7. 4Direct Proof
8. 5Proof by the Contrapositive
9. 6Proof by Exhaustion
10. 7Disproof by Counterexample
11. 8Proving Existence and Uniqueness
12. 9The Triangle Inequality
13. 10The Arithmetic Mean–Geometric Mean Inequality
14. 11The Cauchy–Schwarz Inequality
15. 12Polynomial, Exponential and Logarithmic Growth
16. Named Inequalities (10)
17. 13Working Backwards from the Goal
18. 14Solving a Simpler Problem First
19. 15From a Special Case to Every Case
20. 16Finding the Flaw in an Argument
21. Problem Solving (10)