Linear Algegra Help?

Question

The set of points on the plane with integer coordinates over the filed of real numbers do not form a vector space because while there is closure for vector addition, there is no closure for scalar multiplication.
(1/2) • (1,3) = (1/2, 3/2)
Why can't you define the scalars as a set of integers?

Answer 1

Look at the definition of "over the field of real numbers."

AND: Do the set of integers form a field?