In Spivak's Calculus, Chapter 1, pg 12, theorem 1, it says that in order to prove that theorem: |a + b| <= |a| + |b|...there are 4 cases of what could happen...blah, blah.
So one of the cases supposes that a >= 0 and b <= 0. Then it goes on to say something like "In this case, we must prove...