\bigl & \bigr etc (LaTeX2e unofficial reference manual (November 2018))

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#### 16.2.5.2 `\bigl`, `\bigr`, etc.

Synopsis, one of:

    \bigldelimiter1 ... \bigrdelimiter2
    \Bigldelimiter1 ... \bigrdelimiter2
    \biggldelimiter1 ... \biggrdelimiter2
    \Biggldelimiter1 ... \Biggrdelimiter2

(as with `\bigl[...\bigr]`; strictly speaking they need not be paired, see below), or one of:

    \bigmdelimiter
    \Bigmdelimiter
    \biggmdelimiter
    \Biggmdelimiter

(as with `\bigm|`), or one of:

    \bigdelimiter
    \Bigdelimiter
    \biggdelimiter
    \Biggdelimiter

(as with `\big[`).

Produce manually-sized delimiters. For delimiters that are automatically sized see \left & \right).

This produces slightly larger outer vertical bars.

      \bigl| |x|+|y| \bigr|

The commands above are listed in order of increasing size. You can use the smallest size such as `\bigl...\bigr` in a paragraph without causing LaTeX to spread the lines apart. The larger sizes are meant for displayed equations.

See Delimiters for a list of the common delimiters. In the family of commands with ‘`l`’ and ‘`r`’, delimiter1 and delimiter2 need not be the same.

The ‘`l`’ and ‘`r`’ commands produce open and close delimiters that insert no horizontal space between a preceding atom and the delimiter, while the commands without ‘`l`’ and ‘`r`’ insert some space (because each delimiter is set as an ordinary variable). Compare these two.

    \begin{tabular}{l}
      \(\displaystyle \sin\biggl(\frac{1}{2}\biggr) \)  \\  % good
      \(\displaystyle \sin\bigg(\frac{1}{2}\bigg)  \)   \\  % bad
    \end{tabular}

The traditional typographic treatment is on the first line. On the second line the output will have some extra space between the `\sin` and the open parenthesis.

Commands without ‘`l`’ or ‘`r`’ do give correct spacing in some circumstances, as with this large vertical line

    \begin{equation}
      \int_{x=a}^b x^2\,dx = \frac{1}{3} x^3 \Big|_{x=a}^b
    \end{equation}

(many authors would replace `\frac` with the `\tfrac` command from the `amsmath` package), and as with this larger slash.

    \begin{equation}
      \lim_{n\to\infty}\pi(n) \big/ (n/\log n) = 1
    \end{equation}

Unlike the `\left...\right` pair (see \left & \right), the commands here with ‘`l`’ and ‘`r`’ do not make a group. Strictly speaking they need not be matched so you can write something like this.

    \begin{equation}
      \Biggl[ \pi/6 ]
    \end{equation}

The commands with ‘`m`’ are for relations, which are in the middle of formulas, as here.

    \begin{equation}
      \biggl\{ a\in B \biggm| a=\sum_{0\leq i<n}3i^2+4 \biggr\}
    \end{equation}

Unofficial LaTeX2e reference manual