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Math Help - Properties of the real numbers

  1. #1
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    Properties of the real numbers

    For a, b in R, prove:
    -(-a)=a
    (-a)(-b)=ab
    -(a/b)=(-a)/b if b is nonzero

    how do I even approah this?
    For the first one, I have -a+a=0 so -(-a)=a, but that seems way too simple and like it's not doing anything to prove anything. Thank you for any help!
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  2. #2
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    Quote Originally Posted by sfitz View Post
    For a, b in R, prove:
    -(-a)=a
    (-a)(-b)=ab
    -(a/b)=(-a)/b if b is nonzero

    how do I even approah this?
    For the first one, I have -a+a=0 so -(-a)=a, but that seems way too simple and like it's not doing anything to prove anything. Thank you for any help!
    WE have:

    -a + (-(-a)) = 0 and also a + (-a) =0 and from these two equations by using the cancellation law : if a +b = a +c then b =c we get;

    a = -(-a).

    we also have:

    (-a)(-b) = (-1)a(-b) = a((-1)(-b)) = a(-(-b)) = ab ,since (-1)x = -x.

    And for the last one we have: =

    -(a/b) = - a\frac{1}{b} = (-1)(a \frac{1}{b}) = (-a)\frac{1}{b} = \frac{-a}{b}
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