This sort of contradiction by infinite descent is not uncommon: e.g. the textbook proofs of Fermat’s last theorem for n = 3 and 4, or the proof that a periodic

This sort of contradiction by infinite descent is not uncommon: e.g. the textbook proofs of Fermat’s last theorem for n = 3 and 4, or the proof that a periodic crystal lattice can only have symmetry axes of order {1,2,3,4,6}.