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In the following question here the notation $c\in ]a,b[$ is used. What does this mean? I have never seen it before.

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    The notation is especially common when there is the possibility of confusing the ordered pair $(a,b)$ with the interval $(a,b)$. Using $]a,b[$ for the interval eliminates this possibility.2012-11-26
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    To complement the answers below, square brackets are used to indicate ends of intervals, so $[a,b]$, $[a,b[$, $]a,b]$ and $]a,b[$ mean the closed interval, the half-closed (or "half-open") interval with $b$ excluded, the half-closed interval with $a$ excluded, and the open interval, respectively, all with end-points $a$ and $b$. As already mentioned, this notation (due to Bourbaki) avoids ambiguity by being different from the notation used for ordered pairs.2012-11-26

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