Let G 1 be a field and let V be a vector space over G 1 . There exists a finite subset of V which is a basis of V . A is finite.
V is finite dimensional.
If V is finite dimensional, then W is finite dimensional. Let G 1 be a field and let V be a vector space over G 1 . Note that there exists a subspace of V which is strict and finite dimensional. Let G 1 be a field and let V be a finite dimensional vector space over G 1 . One can check that every subspace of V is finite dimensional.