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I'm not a student with a math background. I don't understand the meaning of a notation of upward or downward arrow, i.e. $\downarrow$ or $\uparrow$, and in which way are these notations different from $\rightarrow$ or $\leftarrow$? For example, in this sentence:

We cannot exclude the possibility that an equation with $f(x)\downarrow 0$ and a divergence $g(x) \uparrow \infty $ as $x\downarrow 0$ might have dynamic solutions.

Thank you very much and many sorry if this question is too silly.

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1 Answer

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They mean a one sided limit. "$f(x) \downarrow 0$" means that $f(x)$ is going to $0$ from above, for example if $f(x)=x^2$ and you're taking limit $x$ to $0$ then $f(x) \downarrow 0$ (because $f(x)$ is never negative).

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