Is the set of integers a vector space?

My friend says it's not, because he thinks vectors have to have have at least two elements, otherwise they're scalars. I say that (Z, +, *) satisfies the axioms of a vector space and that's all you need.

What does /sci/ think?

A vector only needs a magnitude and direction. A scalar has only a magnitude. I'd think you could argue that any vector is made up of one dimensional components which themselves have to be vectors in order to maintain a relationship between themselves and the others.