 Suppose that "X" is a normed vector space and let "E" be any non-empty subset of "X".The closed linear span of "E", denoted by formula_3 or formula_4, is the intersection of all the closed linear subspaces of "X" which contain "E".One mathematical formulation of this is

The closed linear span of the set of functions "xn" on the interval [0, 1], where "n" is a non-negative integer, depends on the norm used.