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?

>>15
Fine, it's true that >>10 didn't define a norm.  Nevertheless, most obvious definitions of norm for vector spaces would give it a value of 0.

>>16
Your general understanding is correct.  However, "not all (in fact, only two) of its elements have multiplicative inverses" is wrong.  The only element of Z with a multiplicative inverse in Z is 1 (1/2 is the multiplicative inverse of 2, but it is definitely not in Z).