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I know $[0,1]$ denotes the interval between 0 and 1 with the boundary. And $(0,1)$ denotes the interval between 0 and 1 without the boundary. Today, I encounter some expressions as $]0,1]$, $]-\infty,+\infty]$. What does $]0,1]$ mean? Thanks.

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Using a reverse $]$ is what some people do instead of a round $($. So $]0,1[$ means the same as $(0,1)$, and in your example, $]0,1]$ means the same as $(0,1]$.

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