TITLE: Arrow in limit operator
QUESTION [7 upvotes]: In this Wikipedia article, I see a limit operator such as in:
$$\lim_{x \searrow 0} \frac{e^{-1/x}}{x^m}=0\,\,;\,\,\,\, m\in \mathbb{N}$$
I am assuming that the downward pointing arrow indicate the limit as $x$ approaches $0$ from the positive direction? Is this conventional? I've seen both 
$\displaystyle\lim_{x \rightarrow 0⁺}$ and $\displaystyle\lim_{x \downarrow 0}$, but never before $\displaystyle\lim_{x \searrow 0}$

REPLY [4 votes]: Yes, it means that considers decreasing sequences that converge to 0.
I've only once worked with someone who preferred to use the $ \searrow$ and $\nearrow$ notation, but it's a good notation in the sense that it takes only a moment to become completely confident in what it means. That's one of the best parts of writing out math, I think - we can invent our own notation so long as it follows intuitive guidelines (rather than very strict, traditional guidelines) in many cases.