Proofs & Logic — How We Know
Logical statements, implication & contrapositive, direct proof, counterexamples, and proof by induction.
Every result in this whole track is certain because it was proved. This course is about how — the rules of airtight reasoning that turn "it seems true" into "it must be true." It is the bridge from arithmetic to real mathematics.
- 01 Statements & logic ELI5: a statement is a sentence that is definitely true or false (never both). We build bigger ones with and (needs both) and or (needs at least one). The…
- 02 Implication, converse & contrapositive ELI5: "if P then Q" is the shape of every theorem. Two cousins to keep straight: the contrapositive "if not Q then not P" is always…
- 03 Direct proof & counterexamples ELI5: a direct proof argues straight from definitions: "the sum of two even numbers is even" because 2a + 2b = 2(a + b), which is divisible by 2. The…
- 04 Proof by induction ELI5: induction is the domino effect — show the first domino falls, and that each domino topples the next, and you've proved all of them fall. A favourite:…