Yes. Choose the principal ultrafilter at any $j\geq2$. Evaluation at the $j$th coordinate gives
$$
\prod_{i\in\mathbb N}\mathcal C_i/\mathcal U\cong\mathcal C_j,
$$
which is a finite <cyclic group> of order $j$.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 144 / 2 / c / i / Solution

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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-144/2/c/i/solution