vaidiarte

How can I show the set of integers Z cannot be made into a vector space over R? Z=(0, +-1, +-2,...) For example I had to show how the set of integers Z cannot be made into a vector space over C by: (i) exits in V and a vector (1) exits in Z i*1=i therefore, i does not exists in Z Hence it is not a vector space because it does not close under scalar mulitplication. I have to do the same with rationals (Q) and with reals®