Big Union in LaTeX (\bigcup)

Where it is used

Large union operator for the union of an indexed family of sets, with limits above and below.

\bigcup_{i=1}^{\infty} A_i writes a countable union, and \bigcup_{\alpha \in I} U_\alpha a union over an index set, as in open covers. It behaves like \sum: limits go below and above in display style and to the side inline, and \limits forces them below inline. Do not use it between two sets; A \cup B uses the binary \cup. Related large operators include \bigcap, \bigsqcup for disjoint unions, and \biguplus for multiset union. De Morgan's laws pair it with \bigcap and complements.

Also listed under: Summation & Product

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Big Union: $\bigcup$

\[ \bigcup_{n=1}^{\infty} \left[ \frac{1}{n}, 1 \right] = (0, 1] \]
\end{document}

Related symbols

• Big Intersection\bigcap
• Intersection\cap
• Set Minus\setminus
• Union\cup
• Complement\complement
• Superset or Equal\supseteq

Frequently asked questions

How do I write Big Union in LaTeX?

Type \bigcup in math mode, for example $\bigcup_{n=1}^{\infty} \left[ \frac{1}{n}, 1 \right] = (0, 1]$. It works in plain LaTeX without loading any package.

Which package do I need for \bigcup?

None. \bigcup is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \bigcup in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\bigcup$ in running text. If you only need the glyph in text, paste the Unicode character ⋃ instead (with XeLaTeX or LuaLaTeX and a font that has it).