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
Fail. A norm is implicitly defined with the scalar multiplication.    If you actually need the definition of the norm, here it is: ||0||=0.  Feel better?  (Just like 17 said.)

{0} is commonly known as "the trivial vector space".  It is a subspace of every vector space, and it IS a vector space.