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Thread: -(a + b) = -a-b

  1. #1
    Nov 2008

    -(a + b) = -a-b

    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:

    -(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
    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.

    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?

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  2. #2
    Dec 2007
    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.
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