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Master all types of brackets and parentheses in LaTeX mathematical expressions. This comprehensive guide covers everything from basic parentheses to advanced delimiter sizing techniques, with visual examples for every concept.
Quick start: LaTeX provides various bracket types and automatic sizing with \left and \right. For basic parentheses use (), for square brackets [], and for curly braces \{\}.Prerequisites: Basic LaTeX math mode knowledge. See Mathematical Expressions for math mode basics.

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What You’ll Learn

  • ✅ All bracket and delimiter types in LaTeX
  • ✅ Automatic sizing with \left and \right
  • ✅ Manual size control for fine-tuning
  • ✅ Multi-line equations with balanced delimiters
  • ✅ Special cases and advanced techniques
  • ✅ Common errors and how to fix them
  • ✅ Best practices for readable mathematics

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Types of Brackets and Delimiters

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Complete Visual Reference

TypeLaTeX CodeOutputCommon Use
Parentheses( )( )( \, )General grouping
Square brackets[ ][ ][ \, ]Arrays, intervals
Curly braces\{ \}{ }\{ \, \}Sets, systems
Angle brackets\langle \rangle⟨ ⟩\langle \, \rangleInner products
Vertical bars| or \vert∣ ∣\lvert \, \rvertAbsolute value
Double bars|| or \Vert∥ ∥\lVert \, \rVertNorms
Floor\lfloor \rfloor⌊ ⌋\lfloor \, \rfloorFloor function
Ceiling\lceil \rceil⌈ ⌉\lceil \, \rceilCeiling function

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Basic Examples

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Parentheses
$(a + b)$

% Square brackets  
$[x, y]$

% Curly braces (must be escaped)
$\{z : z > 0\}$

% Angle brackets
$\langle u, v \rangle$

% Absolute value
$|x - y|$

% Norm
$\|v\|$

% Floor and ceiling
$\lfloor x \rfloor$ and $\lceil x \rceil$

\end{document}

Rendered Output

Parentheses: (a+b)(a + b)Square brackets: [x,y][x, y]Curly braces: {z:z>0}\{z : z > 0\}Angle brackets: ⟨u,v⟩\langle u, v \rangleAbsolute value: ∣x−y∣|x - y|Norm: ∥v∥\|v\|Floor and ceiling: ⌊x⌋\lfloor x \rfloor and ⌈x⌉\lceil x \rceil

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Automatic Delimiter Sizing

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The \left and \right Commands

LaTeX can automatically size delimiters to match their content using \left and \right: 
\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Without automatic sizing
$(\frac{1}{2})$

% With automatic sizing
$\left(\frac{1}{2}\right)$

% Works with any delimiter type
$\left[\frac{x^2}{y}\right]$

$\left\{\sqrt{\frac{a}{b}}\right\}$

$\left|\sum_{i=1}^n x_i\right|$

% Nested fractions
$\left(\frac{\frac{a}{b}}{\frac{c}{d}}\right)$

\end{document}

Rendered Output

Without sizing: (12)(\frac{1}{2})With sizing: (12)\left(\frac{1}{2}\right)Square brackets: [x2y]\left[\frac{x^2}{y}\right]Curly braces: {ab}\left\{\sqrt{\frac{a}{b}}\right\}Absolute value: ∣∑i=1nxi∣\left|\sum_{i=1}^n x_i\right|Nested fractions: (abcd)\left(\frac{\frac{a}{b}}{\frac{c}{d}}\right)

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Important Rules for \left and \right

Critical: Every \left must have a matching \right in the same math environment. They must be balanced like opening and closing HTML tags.

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Invisible Delimiters

Sometimes you need an invisible delimiter to balance the equation: 
% Using \right. for invisible right delimiter
$\left\{\begin{array}{ll}
x + y = 1 \\
x - y = 0
\end{array}\right.$

% Using \left. for invisible left delimiter
$\left.\frac{dy}{dx}\right|_{x=0}$

Rendered Output

System with invisible right delimiter: {x+y=1x−y=0\left\{\begin{array}{ll} x + y = 1 \\ x - y = 0 \end{array}\right.Evaluation bar with invisible left delimiter: dydx∣x=0\left.\frac{dy}{dx}\right|_{x=0}

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Manual Size Control

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Size Commands

When automatic sizing doesn’t give the desired result, use manual size commands:
Delimiter Size Commands (smallest to largest):
CommandSize
\big50% larger than normal
\Big2× normal size
\bigg2.5× normal size
\Bigg3× normal size

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Size Comparison

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Normal size
$( \frac{1}{2} )$

% \big
$\big( \frac{1}{2} \big)$

% \Big
$\Big( \frac{1}{2} \Big)$

% \bigg
$\bigg( \frac{1}{2} \bigg)$

% \Bigg
$\Bigg( \frac{1}{2} \Bigg)$

% For opening and closing separately
$\bigl( x \bigr)$  % 'l' for left, 'r' for right

\end{document}

Rendered Output

SizeResult
Normal(12)( \frac{1}{2} )
\big(12)\big( \frac{1}{2} \big)
\Big(12)\Big( \frac{1}{2} \Big)
\bigg(12)\bigg( \frac{1}{2} \bigg)
\Bigg(12)\Bigg( \frac{1}{2} \Bigg)

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Left and Right Variants

Use l and r suffixes for proper spacing: \bigl(, \bigr), \Bigl[, \Bigr], etc. This ensures correct spacing around the delimiters.

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Advanced Techniques

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Nested Brackets

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Poor: all brackets same size
$[1 + [2 + [3 + 4]]]$

% Better: graduated sizes
$\Big[1 + \big[2 + [3 + 4]\big]\Big]$

% Best: automatic sizing
$\left[1 + \left[2 + \left[3 + 4\right]\right]\right]$

% Complex nesting
$\left\{x : \left[a + \left(\frac{b}{c}\right)\right] > 0\right\}$

\end{document}

Rendered Output

Poor (all same size): [1+[2+[3+4]]][1 + [2 + [3 + 4]]]Better (graduated sizes): [1+[2+[3+4]]]\Big[1 + \big[2 + [3 + 4]\big]\Big]Best (automatic sizing): [1+[2+[3+4]]]\left[1 + \left[2 + \left[3 + 4\right]\right]\right]Complex nesting: {x:[a+(bc)]>0}\left\{x : \left[a + \left(\frac{b}{c}\right)\right] > 0\right\}

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Multi-line Equations with Brackets

For equations that span multiple lines, you need special handling: 
\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Using \right. and \left. for invisible delimiters
\begin{align}
f(x) = & \left[ x^2 + 2x \right. \\
       & \left. + 1 \right]
\end{align}

% Alternative using \big commands
\begin{align}
g(x) = & \Big[ x^3 + 3x^2 \\
       & \phantom{\Big[} + 3x + 1 \Big]
\end{align}

% For cases/piecewise functions
\begin{equation}
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x^2 & \text{if } x < 0
\end{cases}
\end{equation}

\end{document}

Rendered Output

Piecewise function with cases: f(x)={x2if x≥0−x2if x<0f(x) = \begin{cases} x^2 & \text{if } x \geq 0 \\ -x^2 & \text{if } x < 0 \end{cases}

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Matrix Delimiters

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Different matrix environments
$\begin{pmatrix}  % parentheses
a & b \\
c & d
\end{pmatrix}$

$\begin{bmatrix}  % brackets
a & b \\
c & d
\end{bmatrix}$

$\begin{Bmatrix}  % braces
a & b \\
c & d
\end{Bmatrix}$

$\begin{vmatrix}  % vertical bars
a & b \\
c & d
\end{vmatrix}$

$\begin{Vmatrix}  % double bars
a & b \\
c & d
\end{Vmatrix}$

\end{document}

Rendered Output

pmatrix (parentheses): (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}bmatrix (brackets): [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}Bmatrix (braces): {abcd}\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}vmatrix (vertical bars): ∣abcd∣\begin{vmatrix} a & b \\ c & d \end{vmatrix}Vmatrix (double bars): ∥abcd∥\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}

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Special Use Cases

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Set Notation

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Basic set
$A = \{1, 2, 3, 4, 5\}$

% Set builder notation
$B = \{x \in \mathbb{R} : x^2 < 4\}$

% Set with conditions
$C = \left\{x \in \mathbb{Z} : \begin{array}{l}
x > 0 \\
x \text{ is even}
\end{array}\right\}$

% Empty set
$\emptyset = \{\}$

\end{document}

Rendered Output

Basic set: A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\}Set builder notation: B={x∈R:x2<4}B = \{x \in \mathbb{R} : x^2 < 4\}Empty set: ∅={}\emptyset = \{\}

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Interval Notation

\documentclass{article}
\usepackage{amsmath}
\begin{document}

% Open interval
$(a, b)$

% Closed interval
$[a, b]$

% Half-open intervals
$[a, b)$ and $(a, b]$

% Infinite intervals
$(-\infty, a]$ and $[b, \infty)$

% Union of intervals
$[0, 1] \cup [2, 3]$

\end{document}

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Physics and Engineering

\documentclass{article}
\usepackage{amsmath}
\usepackage{physics} % provides \bra, \ket, \braket
\begin{document}

% Quantum mechanics bra-ket notation
$\langle \psi | \phi \rangle$

% With physics package
$\bra{\psi}\ket{\phi}$
$\braket{\psi|\phi}$

% Commutator
$[A, B] = AB - BA$

% Anticommutator  
$\{A, B\} = AB + BA$

% Poisson bracket
$\{f, g\} = \sum_i \left(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i} - \frac{\partial f}{\partial p_i}\frac{\partial g}{\partial q_i}\right)$

\end{document}

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Common Errors and Solutions

Problem: Every \left needs a matching \right, even across line breaks.Solution: Use \right. for an invisible right delimiter:
\left[ x + y \right.  % End of first line
\left. + z \right]    % Start of second line
Problem: Automatic sizing makes brackets unnecessarily large.Solution: Use manual sizing instead:
% Instead of
$\left( \sum_{i=1}^n x_i \right)$

% Use
$\bigg( \sum_{i=1}^n x_i \bigg)$
Problem: { and } have special meaning in LaTeX.Solution: Escape them with backslash:
$\{ x : x > 0 \}$  % Correct
${ x : x > 0 }$    % Wrong - braces disappear
Problem: Brackets don’t match across aligned lines.Solution: Use phantom brackets:
\begin{align}
f(x) = & \Big[ x^2 + 2x \\
       & \phantom{\Big[} + 1 \Big]
\end{align}

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Best Practices

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1. Choose the Right Delimiter

Good Delimiter Choices:
  • Parentheses: General grouping, function arguments
  • Square brackets: Matrices, commutators, intervals
  • Curly braces: Sets, systems of equations
  • Angle brackets: Inner products, averages
  • Vertical bars: Absolute values, determinants, norms

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2. Sizing Guidelines

  • Use \left...\right for complex expressions with varying heights
  • Use manual sizing (\big, \Big, etc.) for simple expressions
  • Be consistent within the same document
  • Don’t oversize—readability is key

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3. Spacing Considerations

% Good spacing with \bigl and \bigr
$\bigl( x + y \bigr)$

% Poor spacing with just \big
$\big( x + y \big)$

% For better spacing around bars
$\left\lvert x \right\rvert$  % Better than |x|

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4. Semantic Markup

Use meaningful commands when available: 
% Instead of manual brackets
$|| v ||$

% Use semantic commands
$\lVert v \rVert$      % Double bars for norm
$\lvert x \rvert$      % Single bars for absolute value
$\langle u, v \rangle$ % Angle brackets for inner product

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Quick Reference Card

CategoryCommandsResult
Parentheses( )(x)(x)
Square brackets[ ][x][x]
Curly braces\{ \}{x}\{x\}
Angle brackets\langle \rangle⟨x⟩\langle x \rangle
Vertical bars| or \vert∣x∣\lvert x \rvert
Double bars|| or \Vert∥x∥\lVert x \rVert
Floor\lfloor \rfloor⌊x⌋\lfloor x \rfloor
Ceiling\lceil \rceil⌈x⌉\lceil x \rceil
Auto sizing\left( \frac{1}{2} \right)(12)\left(\frac{1}{2}\right)
Manual sizing\Big( x \Big)(x)\Big( x \Big)

Mathematical Expressions

Learn math mode basics and expressions

Matrices Guide

Complete guide to matrices and arrays

Equations

Multi-line and numbered equations

Math Symbols

Comprehensive symbol reference
LaTeX Cloud Studio automatically handles package loading! The amsmath package is pre-loaded, so all bracket commands work immediately without manual package management.