Sets and Proof
Map
Arrows point from what you learn first to what it opens. Right-click a concept (or press and hold it) for its lessons and stories.
- Proven to depth123
- Open
- Locked
- Comes back deeper
Learning path
In the order the concepts build on each other.
- Mathematical proofLockedAn argument that shows why a statement is true in every case, not just the ones checked. Checking examples, however many, is never enough, and one counterexample is enough to break a claim.Opens after: Even and odd numbers, Counterexample
- ConjecturesLockedA statement mathematicians believe and have checked on many examples, but have not proved - like Goldbach's conjecture that every even number bigger than 2 is two primes added together.Opens after: Prime numbers, Mathematical proof
Connections to other domains
- Mathematical proof leads to Prime numbersNumber Theory
- Conjectures needs Prime numbersNumber Theory
- Mathematical proof needs Even and odd numbersArithmetic
- Mathematical proof needs CounterexampleLogic