Looking at the various axioms for vector spaces, I'm getting hung up on this one: 

> 
> Additive Identity  
> 
>  The set $V$ contains an additive identity element, denoted by $0$, such that for any vector $v$ in V, $0 + v = v$ and $v + 0 = v$. 
> 
> 
> 

It seems simple enough but in an example given - 

$V = \Bigg\{
\begin{bmatrix}
1+x\\2-x\\3+2x
\end{bmatrix} 
\Bigg| x \in \mathbb{R}\Bigg\}$ 

And the additive identity is -  

$0=\begin{bmatrix}
1\\2\\3
\end{bmatrix}$ 

I'm confused by this as certainly, $v + 0 \neq v$. 

I'd appreciate any help in understanding this, thanks!