The Diagonal Argument

Uncountably many reals

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Cantor’s diagonal argument: any list of real numbers misses some.
• The real numbers are uncountable, a bigger infinity than the counting numbers.
• There is an endless hierarchy of infinities.

Steps

1. List all decimals?
2. Build a missing number
3. Your turn
4. Beat the list
5. Uncountable
6. Which are countable?
7. Subsets win
8. Between the two?