I'm wondering what is the difference in the use of
$\lim\limits_{x \downarrow a}$
$\lim\limits_{x \searrow a}$ $\lim\limits_{x \nearrow a}$
$\lim\limits_{x \uparrow a}$
I see them around and I don't know what they really mean. Do the arrows characterize how $x$ tends to $a$?