Theorem: 1 - 1 = 0 (trivial-group orbit count)

Theorem (Burnside-trivial canonical): for the trivial group G = {e} acting on any set X, the Burnside / Cauchy-Frobenius lemma gives # orbits = (1/|G|) sum_g |Fix(g)| = |Fix(e)|/1 = |X|. For X = {single point}: # orbits = 1, so the…