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Is there any logic or justification for the notation $(a,b)$ to represent $]a,b[$? To me this notation is very ambiguous and confusing because it looks like a couple of numbers and not an interval.

Thanks.

Martin Sleziak
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    But when you talk about real numbers, you don't think about $(a,b)$ as a point in $\mathbb R^2$, right? I guess in most cases, there will be no confusion with proper context. – Troy Woo Sep 14 '14 at 11:43
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    It's just a matter of convention, I was confused too when I first saw the notation $(a,b)$ because in italian schools they usually teach the square brackets ones, but once you know that they are equivalent I don't think there can be any ambiguity, based on the context – Alessandro Codenotti Sep 14 '14 at 11:47
  • The first seems to be common in US, the second - in France (and few other European countries, big and small). The advantage of the second notation is that you cannot mistake it for the ordered pair notation $(a,b)$! – Moishe Kohan Sep 14 '14 at 12:00
  • I agree that $(a,b)$ is in theory confusing although in practice there is rarely ever an issue. I personally think that $]a,b[$ or $[a,b[$ look rather ugly compared to $(a,b)$ or $[a,b)$. – Frunobulax Sep 14 '14 at 12:41
  • These questions are (to some extent) related: http://math.stackexchange.com/questions/430851/notation-for-intervals and http://math.stackexchange.com/questions/653425/whats-the-difference-between-a-b-and-a-b – Martin Sleziak Sep 14 '14 at 12:49
  • That is precisely the reason why the notation I was taught for intervals uses semicolons. Hence, $(a; b)$ for open interval, $[a; b]$ for closed, and so forth. – Ken Jun 03 '15 at 14:40

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