1/x has oscillation ∞ at x = 0, and oscillation 0 at other finite x and at −∞ and +∞. sin (1/x) (the topologist's sine curve) has oscillation 2 at x = 0, and 0 elsewhere. sin x has oscillation 0 at every finite x, and 2 at −∞ and +∞. The sequence 1, −1, 1, −1, 1, −1, ... has oscillation 2.