I think he means the integers are opposites. In other words, if y= -x, then x is the opposite of y. Therefore x= -y and x + y =0. Think of it with numbers. If x = 2, then y = -2 (opposite). If you add opposites you get 0.
I'm trying to work my way through Basic Mathematics by Serge Lang and am already stuck on page 11!
The part I'm stuck at goes:
I think I can somewhat see the reasoning behind this. If the negation of expression a is equal to expression b, then expression a without the negation, added to expression b, will be 0.-(a + b) = -a - b
Proof. Remember that if x, y are integers then x = -y and y = -x mean that x + y = 0. Thus to prove our assertion, we must show that
(a + b) + (-a - b) = 0
What I'm having trouble understanding is what he means by x and y in this particular case. Does he mean the two expressions? If so, can somebody please point out how the expressions map to x and y?