Scalars and determining subspaces

[MoreDrinks]

To determine if a subset of a vector space is a subspace, it must be closed under addition and scalar multiplication. As far as I can tell, this means adding two arbitrary vectors in the subset and having the sum be within the subset.

But...can the scalar be any number? Is there any limitation?

 

[micromass]

If $W$ is a subspace of $V$, then $\alpha v\in W$ for any scalar $\alpha$ and for any $w\in W$.

 

[MoreDrinks]

If $W$ is a subspace of $V$, then $\alpha v\in W$ for any scalar $\alpha$ and for any $w\in W$.

Thanks, my book is terrible.