In a test I was asked to give a definition to a subspace to a vector space, I wrote:
A subset $V$ is a subspace of $X$ if $0 \in V$ and $\forall u,v \in V, > \exists \thinspace V$ s.t. $ u+v = 0$
I was told that it is not correct. The correct definition is that the subset is closed under addition and closed under scalar multiplication.
Why is the second set of definition "more" correct than the definition I gave?