The vanishing of the Pontryagin classes and Stiefel–Whitney classes of a vector bundle does not guarantee that the vector bundle is trivial. For example, up to vector bundle isomorphism, there is a unique nontrivial rank 10 vector bundle formula_16 over the 9-sphere. (The clutching function for formula_16 arises from the homotopy group formula_18.) The Pontryagin classes and Stiefel-Whitney classes all vanish: the Pontryagin classes don't exist in degree 9, and the Stiefel–Whitney class "w"9 of "E"10 vanishes by the Wu formula "w"9 = "w"1"w"8 + Sq1("w"8). Moreover, this vector bundle is stably nontrivial, i.e. the Whitney sum of "E"10 with any trivial bundle remains nontrivial.