Proof by Contradiction

√2 is irrational

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Proof by contradiction: assume the opposite and derive something impossible.
• $\sqrt2$ is irrational: assuming $\frac{a}{b}$ in lowest terms forces both $a$ and $b$ to be even.
• Examples can disprove a general claim, but they can never prove one.

Steps

1. The idea
2. Even squares
3. √2 is irrational
4. Rebuild the proof
5. A proof you can see
6. Close, but never equal
7. No largest