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?

>>11
lol - touche
0 is definitely a magnitude.

The trivial vector space is still a good reminder that the typical high school teacher definition of vectors as "magnitude and direction" is a gimmick to avoid formalism.