The question above is really it. The reason I ask is that my text says a vector space can have more than one zero vector (It's a true/false question: A vector space may have more than one zero vector). But if the zero vector in any space is unique, then it has only one zero vector, no?
Or am I reading "unique" wrong?
Best Answer
By unique we can say that there is only one zero vector. To see this, Suppose that we have a vector space with two zero vectors, $x,x'$, then we have
$$ x = x+x' = x' + x = x'. $$
Thus the zero vector is indeed unique.