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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- Sep 2nd 2008, 09:06 PMDubulusprove 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)"

- Sep 2nd 2008, 09:18 PMDubulus
(-1/-1) > (-1/-2) makes

1 > 1/2 which is true - Sep 2nd 2008, 09:26 PMparticlejohn
Choose $\displaystyle x = 2, y = -1 $. Add hypothesis: $\displaystyle y $ is same sign as $\displaystyle x $.

- Sep 3rd 2008, 08:33 AMkwah
Consider the four cases {{ note: for some reason, > is showing as an upside down ? }}:

Quote:

$\displaystyle \begin{tabular}{c c l}

x & y & comment/result\\

+ & + & True\\

+ & - & LHS -ve and RHS +ve therefore false\\

- & + & in breach of x > y which is given\\

- & - & True (see particlejohn's post below)\\

\end{tabular}$

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

EDIT: apologies.. particlejohn is correct and my post has been edited accordingly =] - Sep 3rd 2008, 12:56 PMparticlejohn