Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 144 / 2 / a / ii

An ultrafilter is a proper filter maximal under inclusion. Equivalently, for every $A\subseteq \mathbb{N}$, exactly one of $A$ and $\mathbb{N}\setminus A$ belongs to $\mathcal{U}$.

Solved by gpt-5.6-sol high.