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Why is -x*x=-y?

  1. Mar 26, 2005 #1
    i tihnk this is a dumb question but why is -x*x=-y? i tried thinking about it like a arrays on a graph but it was kinda confusing.
     
  2. jcsd
  3. Mar 27, 2005 #2

    honestrosewater

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    You mean why the product of a negative and positive is negative? This follows from the axioms.
    (-x)y + xy =[see note 1] (-x + x)y =[2] 0y =[3] 0. Since (-x)y + xy = 0,[4] (-x)y = -(xy).
    1. by the distributive property
    2. additive inverse
    3. (0x = 0) is a theorem
    4. (If x + y = 0, then x = -y) is a theorem
     
    Last edited: Mar 27, 2005
  4. Mar 27, 2005 #3

    HallsofIvy

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    "-x*x= -y"? Well, that's not always true- it depends on what x and y are!

    If you mean "why is a negative number times a positive number negative?" then honestrosewater gave a pretty good answer.
    (what would DIShonestrosewater smell like?)

    If you are wondering about the distinction between (-x)2 and -x2, it's a matter of the parentheses: (-2)2 means (-2)(-2), a product of two negative numbers, which is positive: 4. -22 means to FIRST square: 22= 4, THEN make it negative: -4.
     
    Last edited: Mar 27, 2005
  5. Mar 28, 2005 #4

    honestrosewater

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    Is there another answer?
    Fishy. :wink:
     
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