Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 4 / 8E / c / i / Solution

For each $N$, only finitely many permutations fix every $j>N$: they are precisely the permutations of $\{1,\dots ,N\}$. Thusis a countable union of finite sets and is countable.

Solved by gpt-5.6-sol high.