How to input open intervals

Question

I want to write open and half-open intervals using the following notation:

]a, b[
]a, b]
]-∞, b]

When writing them just like that in the LaTeX source, the spacing doesn't come out right. For example, for this equation:

 \(X = ]-\frac{π}{2}, +\frac{π}{2}[\)

the minus sign is typeset as a binary operator. I can solve this by surrounding the whole value in braces, but then the spacing around the equal sign is still not correct. For other combinations of intervals and operators, different spacing inconsistencies arise.

What is the correct and easy way to input intervals in order to avoid having to take care of this at all?

Answer 1

You can use \left] and \right[ then the brackets are taken as delimiters (and also get resized accordantly to the content):

\(X = \left]-\frac{π}{2}, +\frac{π}{2}\right[\)

Answer 2

While I'm a little late to the party, here goes for a slightly more concise solution:

\usepackage{xparse}

\NewDocumentCommand{\INTERVALINNARDS}{ m m }{
    #1 {,} #2
}
\NewDocumentCommand{\interval}{ s m >{\SplitArgument{1}{,}}m m o }{
    \IfBooleanTF{#1}{
        \left#2 \INTERVALINNARDS #3 \right#4
    }{
        \IfValueTF{#5}{
            #5{#2} \INTERVALINNARDS #3 #5{#4}
        }{
            #2 \INTERVALINNARDS #3 #4
        }
    }
}

which allows you to do:

\begin{align*}
    \interval[{a,b}] &&           && \\
    \interval[{a,b}) && \text{or} && \interval[{a,b}[ \\
    \interval({a,b}] && \text{or} && \interval]{a,b}] \\
    \interval({a,b}) && \text{or} && \interval]{a,b}[
\end{align*}

to obtain something like:

Or to use manual or automatic resizing:

\begin{equation*}
    \interval[{a,\infty})[\Bigg] \quad \text{or} \quad
        \interval*[{-\frac{\pi}{2},\frac{\pi}{2}}]
\end{equation*}

to obtain:

Edit: Added the changes suggested by egreg (this was my answer, was just unregistered at the time).

Answer 3

The interval package takes care of the spacing and the scaling of the brackets.

Edit. An example code:

\documentclass{article}
\usepackage{interval}

\begin{document}

    \[ \interval[scaled]{-\frac{\pi}{2}}{\frac{\pi}{2}}\qquad\interval[scaled=\bigg]{-\frac{\pi}{2}}{\frac{\pi}{2}} \]%

\end{document} 

Answer 4

At least two options exist.

---

Option 1: \(X = \left]-\frac{π}{2}, +\frac{π}{2}\right[\)

This works well, even in displaymath mode (\[...\]) since the delimiters are extensible. However, in inline math mode you'll notice the braces may expand more than your liking. For that, use Option 2.

---

Option 2: Wrap the interval in {}: \(X = ]{-\frac{π}{2}, +\frac{π}{2}}[\)

---

Answer 5

Here is a macro which takes care of the spacing and allows you to choose between a resizable version (when followed by a star, for use in display) and a fixed-size version (without a star, for use in text). You have four macros \intervalcc, \intervaloo, \intervaloc and \intervalco for the various types of intervals (o is for open and c for closed):

\documentclass{article}

\makeatletter
\DeclareRobustCommand{\genericinterval}[2]{%
  \@ifstar{\genericinterval@star{#1}{#2}}{\genericinterval@nostar{#1}{#2}}}
\newcommand{\genericinterval@star}[4]{\mathopen{}\mathclose{\left#1#3,#4\right#2}}
\newcommand{\genericinterval@nostar}[4]{\mathopen{#1}#3,#4\mathclose{#2}}
\newcommand{\intervalcc}{\genericinterval[]}
\newcommand{\intervaloo}{\genericinterval][}
\newcommand{\intervaloc}{\genericinterval]]}
\newcommand{\intervalco}{\genericinterval[[}
\makeatother

\begin{document}

$I = \intervalcc{-a^2}{b^2} \cap \intervalcc{-\frac{\pi}{2}}{\frac{\pi}{2}}.$

\[I = \intervalcc{-a^2}{b^2} \cap \intervalcc*{-\frac{\pi}{2}}{\frac{\pi}{2}}.\]

$I = \intervaloo{-a^2}{b^2} \cap \intervaloo{-\frac{\pi}{2}}{\frac{\pi}{2}}.$

\[I = \intervaloo{-a^2}{b^2} \cap \intervaloo*{-\frac{\pi}{2}}{\frac{\pi}{2}}.\]

$I = \intervaloc{-a^2}{b^2} \cap \intervaloc{-\frac{\pi}{2}}{\frac{\pi}{2}}.$

\[I = \intervaloc{-a^2}{b^2} \cap \intervaloc*{-\frac{\pi}{2}}{\frac{\pi}{2}}.\]

$I = \intervalco{-a^2}{b^2} \cap \intervalco{-\frac{\pi}{2}}{\frac{\pi}{2}}.$

\[I = \intervalco{-a^2}{b^2} \cap \intervalco*{-\frac{\pi}{2}}{\frac{\pi}{2}}.\]

\[\intervaloo*{-\frac{\pi}{2}}{\frac{\pi}{2}}^2.\]

\end{document}