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 $a$?
$\endgroup$ 61 Answer
$\begingroup$Arturo Magidin:
$\endgroup$$x↓a$ means that $x$ is approaching a "from above", in a decreasing manner; it's much like $x→a^+$, "approaching from the right"; same for $x↘a$. $x↑a$ means $x$ approaches a from below, in an increasing manner, much like $x→a^−$.
