← Learning Paths

Building the Number Systems

From natural numbers to the Cantor set — building the number systems one by one, filling the gaps from $\mathbb{N}$ to $\mathbb{R}$.

1. Natural Numbers and Induction — 1. Number Systems
2. The Binomial Theorem — 1. Number Systems
3. Integers and Rationals — 1. Number Systems
4. Sets and Functions — 1. Number Systems
5. The Supremum Axiom — 1. Number Systems
6. Countable vs Uncountable — 1. Number Systems
7. Why ℝ Has No Holes — 2. Sequences
8. Construction of the Real Numbers — 2. Sequences
9. Length Zero, Points Uncountable — 4. Topology
10. The Fat Cantor Set — 4. Topology