A way to ensure the existence of limits of certain infinite series is to restrict attention to spaces where any Cauchy sequence has a limit; such a vector space is called complete. Roughly, a vector space is complete provided that it contains all necessary limits. For example, the vector space of polynomials on the unit interval [0, 1], equipped with the topology of uniform convergence is not complete because any continuous function on [0, 1] can be uniformly approximated by a sequence of polynomials, by the Weierstrass approximation theorem. In contrast, the space of all continuous functions on [0, 1] with the same topology is complete. A norm gives rise to a topology by defining that a sequence of vectors \mathbf{v}_n converges to \mathbf{v} if and only if
