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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 $a$?

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    I am still not$a$hundred percent sure whether I understand the difference. Could you give an example of$a$sequence $(x_n)_n$ for which $\lim_{n \to \infty} x_n \neq \lim_{n \uparrow \infty} x_n$?2017-04-13

1 Answers 1

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Arturo Magidin:

$x↓a$ 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 $x→a^−$.