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Which interval is commonly referred to as half closed? Is there any problem if I refer to it as half open?

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    $\begingroup$ Intervals of the form $[a,b)$ and $(a,b]$ are commonly referred to as half-open or half-closed; I usually use the former term, but both are in use. $\endgroup$ – Brian M. Scott May 16 '16 at 16:09
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Both terms have the same meaning but can me interpreted differently (not depending on which term you chose). If the context doesn't imply - which is unlikely to happen - just use $(a,b]$ respectively $[a,b)$ to avoid misunderstandings.

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