# Sergei Yakovenko's blog: on Math and Teaching

## Infinity: first accurate steps

1. Finite and infinite subsets of $\mathbb N$.
2. Admissible infinite operations: infinite unions and intersections. Quantifiers.
3. “Small” and “large” infinite subsets of $\mathbb N$.
4. One-to-one maps as the means of comparison between various infinite sets.
5. The first “paradox”: $\mathbb N\times\mathbb N\simeq\mathbb N$.