Brackets in LaTeX: \left, \right, Absolute Value and Norms

Round, square and curly brackets, bars, and how to make any of them grow to fit. About ten minutes.

Brackets you type go in at their normal size, which is right around $x + 1$ and wrong around a fraction. This lesson is about making them fit, and about the brackets that need a command.

The problem

Typed brackets stay the height of a letter, so they look lost next to anything tall:

(\frac{1}{2})^2

Edit the LaTeX

\left and \right

Put \left before the opening bracket and \right before the closing one, and both grow to fit what is between them:

\left( \frac{1}{2} \right)^2

Edit the LaTeX

They always come in pairs: every \left needs a \right later in the same formula, or LaTeX stops with an error. The two do not have to match, so \left[ 0, 1 \right) is fine.

Square brackets and curly braces

Square brackets work the same way: \left[ ... \right]. Curly braces are different, because LaTeX uses { } for grouping: to print one, put a backslash before it, \{ and \}, or \left\{ and \right\} to make them grow.

\left\{ \frac{1}{n} : n \geq 1 \right\}

Edit the LaTeX

Absolute values and norms

A vertical bar is typed as it is: |x| gives $|x|$ , and \left| ... \right| grows. Two bars for a norm or a length are \|: \|v\| gives $\|v\|$ .

\left| \frac{x - 1}{2} \right| < 1

Edit the LaTeX

One side only

\left. is an invisible bracket, for when only one side should show. The bar used to evaluate an integral is the usual example:

\left. x^2 \right|_0^1 = 1

Edit the LaTeX

Sizes by hand

\left and \right choose a size for you. To choose it yourself, use \big, \Big, \bigg or \Bigg before a bracket, from a little larger to very large: \Big( x \Big). This helps when a bracket opens on one line of a long equation and closes on the next, where \left and \right cannot pair up.

Other brackets

Angle brackets: \langle u, v \rangle gives $\langle u, v \rangle$ .
Floor and ceiling: \lfloor x \rfloor gives $\lfloor x \rfloor$ , and \lceil x \rceil gives $\lceil x \rceil$ .

All of them grow with \left and \right too.

Practise

Where the brackets must grow, plain ones are marked wrong.

$\left( \frac{a}{b} \right)^2$
$\left[ x^2 + \frac{1}{x} \right]$
$|x - 3| < 2$
$\left| \frac{1}{x} \right|$
$\{ x : x > 0 \}$
$\left. x^2 \right|_0^1$
$\langle u, v \rangle$
$\lfloor 2.7 \rfloor = 2$

In short

\left and \right make brackets grow to fit, and always come in pairs.
Curly braces need a backslash: \{ \}. Bars: |x|, and \|v\| for a norm.
\left. is an invisible bracket; \big to \Bigg choose a size by hand.

Next, in lesson 6: sums, integrals and limits.

Brackets that grow

The problem

\left and \right

Square brackets and curly braces

Absolute values and norms

One side only

Sizes by hand

Other brackets

Practise

In short

Would you rather write it by hand?