I may have a bad day, or not enough coffee yet. So, "If A is a nonempty subset of a vector space V, then the set L(A) of all linear combinations of the vectors in A is a subspace, and it is the smallest subspace of V which includes the set A. If A is infinite, we obviously can't use a single finite listing. However, the sum of two linear combinations of elements of A is clearly a finite sum of scalars times elements of A." Question: If A is infinite, how can the sum of its linear combinations be finite (even choosing a finite sum of scalars)? Thank you.