Recent content by MendelCyprys

I'm not a mathematician of any sort so excuse me if my question is stupid. I just realized that I could not define the set of whole numbers without referring back to them or to the operation of addition, which then itself can't be defined. How would you define whole numbers?

First define the dot product for A and B to be the product of their magnitudes and the cosine of the angle between them. We can see geometrically that A.(B + C) = A.B + A.C (think about the component of B and C along A), and therefore (A + B).(C + D) = A.C + A.D + B.C + B.D. Choosing...