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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 $\displaystyle\lim_{x \searrow 0}$

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Yes, all of those notations are the same. This is more often seen in analysis rather than calculus, especially in the context of sequences which are decreasing. –  Jesse Madnick May 2 '11 at 1:00
    
To be clear, x→0+ means approaches from the right, but using any sequence of positive numbers converging to 0 you'd like. Whereas x↘0 means approaches using any decreasing sequence of (positive) numbers converging to 0. I doubt there is much difference. –  Jack Schmidt May 2 '11 at 1:36
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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.

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