Question

How can you prove that b - a is the negative of a - b?

Answer 1

Let a and b be non-negative. Then a => 0 and b => 0. Assume that a + b = 0. Need to show that a = 0. Since a is non-negative, a => 0. Since a + b = 0 we see that a = -b. Since b => 0 we see that -b <= 0. Thus, a <= 0 since a = -b. Since a <= 0 and a => 0 we see that a = 0 as needed to show.