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Question about set notation

Suppose we have that $\ f:]a,b[\rightarrow\mathbb{R}$.

What is $]a,b[$?

I know what $[a,b]$, $(a,b)$, $[a,b)$ are.

I would usually google but I don't know what keyword to use. Let me know if this is too simple/inappropriate for Math.SE and I'll delete.

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marked as duplicate by Andres Caicedo, Thomas, Martin Argerami, Micah, froggie Dec 2 '12 at 21:26

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1  
This $]a,b[$ European notation (French, if I recall correctly) for the open interval $(a,b)$. It's sometimes still used in the literature, but I think parentheses carried the day. –  Alex Nelson Dec 2 '12 at 15:27

1 Answer 1

up vote 12 down vote accepted

$\mathopen]a, b\mathclose[ \;= (a, b)$

$\mathopen]a, b\mathclose[\;\;$ denotes the open interval of real numbers $(a, b)= \{x \in \mathbb{R}: a < x < b\}.$

Such notation is used by some to disambiguate between the ordered pair $(a, b)$ -- which is merely a point in $\mathbb{R}^2$ -- and the open interval $(a, b)\subseteq \mathbb{R}$.

Likewise:

  • $[a, b\mathclose[ = [a, b)$

  • $\mathopen]a, b] = (a, b]$

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Any ideas on how to properly format this in latex? Because $]0,1[\to]0,1[$ looks like it's about some element $[\to]$. –  akkkk Dec 2 '12 at 15:21
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@amWhy: Is this notaion lost in Mathematics contexts? Nice notation. –  B. S. Dec 2 '12 at 15:24
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@akkkk: Use \mathopen and \mathclose, as in \mathopen]a, b\mathclose[. See my edit of the answer. (You can also right click on a formula and use the popup menu to see the LaTeX.) –  Harald Hanche-Olsen Dec 2 '12 at 15:41
    
@Harald That beats brute-force spacing! –  amWhy Dec 2 '12 at 17:03

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