Proof and Logic

Proof is what makes mathematics different from every other subject: a proved statement is true forever, with no exceptions and no doubt. This course teaches the language of logic and sets, then the handful of classic methods of proof that mathematicians use to establish a result beyond argument.

You'll learn to read an implication, tell a necessary condition from a sufficient one, and wield deduction, exhaustion, the killer counterexample, contradiction, and the domino-chain of induction.

Stage 1 — The language

  1. Sets and Set Notation
  2. Logical Statements and Conditions

Stage 2 — Methods of proof

  1. Proof by Deduction
  2. Proof by Exhaustion
  3. Disproof by Counterexample
  4. Proof by Contradiction
  5. Proof by Induction

Let's get started

We begin with the alphabet of rigorous mathematics — sets and the symbols that describe them.

Let's get started → Sets and Set Notation