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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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    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.2012-12-02

1 Answers 1

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

$\mathopen]a, b\mathclose[\;\;$ 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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    @Harald That beats brute-force spacing!2012-12-02