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Math Help - prove inequality

  1. #1
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    prove inequality

    ok heres the prob....the statement below is not always true for x, y (symbol for real numbers). give an example where it is false, and add a hypothesis on y that makes it true. "if x and y are nonzero real numbers and x>y then (-1/x)>(-1/y)"
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  2. #2
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    (-1/-1) > (-1/-2) makes
    1 > 1/2 which is true
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  3. #3
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    Choose  x = 2, y = -1 . Add hypothesis:  y is same sign as  x .
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  4. #4
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    Consider the four cases {{ note: for some reason, > is showing as an upside down ? }}:

    \begin{tabular}{c c l}<br />
x & y & comment/result\\<br />
+ & + & True\\<br />
+ & - & LHS -ve and RHS +ve therefore false\\<br />
- & + & in breach of x > y which is given\\<br />
- & - & True (see particlejohn's post below)\\ <br />
\end{tabular}

    From this, you can see that both x and y must have the same sign.


    EDIT: apologies.. particlejohn is correct and my post has been edited accordingly =]
    Last edited by kwah; September 4th 2008 at 03:46 AM.
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  5. #5
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    Quote Originally Posted by kwah View Post
    Consider the four cases {{ note: for some reason, > is showing as an upside down ? }}:




    From this, you can see that both x and y must be positive.
    Choose  x = -3 and  y = -4 (e.g.  x > y ). Then  \frac{1}{3} > \frac{1}{4} .
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