You're forgetting that there are things other than real numbers: imaginary (or complex) numbers. These are such numbers as the even-powered roots of negative real numbers. Complex numbers exist on a separate vector plane and can be expressed as functions of real numbers of as vectors (modulo-argument form). A real number can also be expressed this way.
Come to think of it, the sum of all vectors may come to zero too. But since woody thinks the answer isn't zero, I wonder what he's getting at. Uhm.
Even with complex numbers you would still come out with zero. Working with a number system like the natural numbers or the integers modulo. The answer could range from 0 to infinity.
Hmmm, this is some new logic of mine, but if you add together all numbers, which include all vectors, imaginary, unreal, real numbers, square roots, etc. the answer will be zero. There is always a negative to positive and a positive to a negative. So with that being said the answer must be zero.
