Difference between \big[ and \bigl[

Question

What is the difference between \big[ (or equivalently \big() and \bigl[? Is it always necessary to mention l (left) and r (right)?

Answer 1

\bigl declares an opening math delimiter with less horizontal spacing than the unspecified \big. \bigr defines a closing math delimiter. Using a \bigl and \bigr pair you could get the brackets or parentheses closer to the term within.

Just compare:

\documentclass{article}
\begin{document}
$\bigl[ \times \bigr]$

$\big[ \times \big]$
\end{document}

Output:

The definitions in latex.ltx are:

\def\bigl{\mathopen\big}
\def\bigm{\mathrel\big}
\def\bigr{\mathclose\big}

Answer 2

You can see the difference in the following example. The left modifiers \bigl etc. are basically \mathopen{}\big. You also have to use \mathopen if you are using \left and \right to do automatic scaling to get correct spacing in some cases.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
  x &= \sin\biggl(\frac12\biggr)          \\ % good
  x &= \sin\mathopen{}\bigg(\frac12\bigg) \\ % good
  x &= \sin\bigg(\frac12\bigg)            \\ % bad
  x &= \sin\left(\frac12\right)           \\ % bad
  x &= \sin\mathopen{}\left(\frac12\right)   % good
\end{align}

\end{document}