Linear algebra doubt Let $V$ be a vector space and $S$ be a non empty subset of it. Can $\operatorname{span}(S)$ contain more number of vectors than in $V$, when 


*

*$S=V$?

*$\operatorname{span}(S)=V$?

No, because your vector space V has to be closed under forming of linear combinations to be a vector space. So every linear combination of elements of V, especially those in S, have to lie already in V. Since the Span of S only exists of linear combinatios i can't 'leave' V with the elements of S. If i consider everything over the same field, that is. 
