Shorthand notation for "increases" and "decreases" I want to write out something like:
"As $x$ increases, $y$ decreases."
Is there a standard symbolic notation for this, such as an up arrow and a down arrow?  (And if you can tell me how to write it in latex, that would be awesome, too).
Thanks!

Inverse proportionality means that 
$y=\frac{k}{x}$ for some constant $k$.
If (as usual) the constant $k$ is positive, then (if $x$ ranges over positive numbers), as $x$ increases, indeed $y$ decreases. 
However, there are many other ways that $y$ can decrease as $x$ increases. For example, we could have 
$$y=\frac{1}{\sqrt{x}},$$
or 
$$y=e^{-x}.$$
There is no really standard symbolic notation for this, but sometimes arrows are used, as in "as $x\uparrow$, $y\downarrow$."  I have also seen slanted arrows used instead, but the standard LaTeX slanted arrows are longer than the arrows I remember seeing.  
