ABSTRACT
Proof: Let {Wi : i ∈ I} be a set of subspaces of V . For w in every Wi, the additive inverse −w is in Wi. Thus, −w lies in the intersection. The same argument proves the other properties of subspaces. ///
The subspace spanned by a set X of vectors in a vector space V is the intersection of all subspaces containing X. From above, this intersection is a subspace.
