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 $a$?