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I was reading a paper which contained the phrase "... for any sequence $c_n \searrow c$ there exists $n_0$ such that ..." I am not familiar with this notation, does $\searrow$ have some common mathematical meaning? elsewhere in the paper, the notation $\nearrow$ is also used in similar context. I tried a google search, but I was unsure which search terms to include in order to find information.

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    $\begingroup$ It means that 1) $\{c_n\}$ converges to $c$, and 2) $\{c_n\}$ is nonincreasing. $\endgroup$ – Umberto P. Jun 2 '16 at 14:29
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It means that $c_n$ converges to $c$ from above.

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As an example $$c_n:=c+\frac1n \searrow c \qquad \text{as}\;\;n \to +\infty$$ while $$c_n:=c-\frac1n \nearrow c \qquad \text{as}\;\;n \to +\infty$$

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