Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
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3@DavidMitra When I first saw it, I thought (incorrectly) that $]a,b[$ meant $\mathbb R\backslash (a,b)$, so I personally don't think this notation is clearer. – Ragnar Jan 27 '14 at 16:10
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@Ragnar I actually agree with you. I also first thought in that way. – Chang Jan 27 '14 at 16:14
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Related question: Notation for intervals – Martin Sleziak Jan 27 '14 at 17:07
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There is no difference. They both refer to "the open interval from $a$ to $b$." The "advantage" of using $]a,b[$ is that it can't be mistaken for an ordered pair.
yoknapatawpha
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and the advantage of $(a,b)$ is that the brackets can't be mistaken to point in the other direction (in more comples expressions) – Hagen von Eitzen Jan 27 '14 at 16:08
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2@HagenvonEitzen I happen to find the $]a,b[$ notation confusing, especially when it's in a longer mathematical expression. But the ability to immediately distinguish $]a,b[$ from an ordered pair is the explanation I've heard for the "backwards bracket" notation from those who do use it (I happen not to be someone who does). – yoknapatawpha Jan 27 '14 at 16:11
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I never liked the $]a,b[$ notation. But it does have the advantage of being visually suggestive as to whether the endpoints are included or not. Same for the closed and half-open variants. The choice of meaning for $(a,b)$ and $[a,b]$ can't be divined from the notation, making that an arbitrary decision about which one means what. – MPW Jan 27 '14 at 17:00