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.
Best Answer
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).