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)"
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)"
Consider the four cases {{ note: for some reason, > is showing as an upside down ? }}:
$\displaystyle \begin{tabular}{c c l}
x & y & comment/result\\
+ & + & True\\
+ & - & LHS -ve and RHS +ve therefore false\\
- & + & in breach of x > y which is given\\
- & - & True (see particlejohn's post below)\\
\end{tabular}$
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 =]