Big Intersection in LaTeX (\bigcap)

Where it is used

Large intersection operator for intersecting an indexed family of sets.

\bigcap_{n=1}^{\infty} (0, 1/n) = \varnothing is a standard example, and topology writes \bigcap_{\alpha} F_\alpha for intersections of closed sets. Like other large operators, its limits sit below and above in display mode and beside it inline, and it scales up in display style. For two sets use the binary \cap instead. Nested intervals, the Cantor set \bigcap_n C_n and the definition of the generated sigma-algebra as the intersection of all containing sigma-algebras all use it.

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}
\usepackage{amssymb}
\begin{document}
Big Intersection: $\bigcap$

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

Related symbols

• Set Minus\setminus
• Big Union\bigcup
• Complement\complement
• Intersection\cap
• Natural Numbers\mathbb{N}
• Union\cup

Frequently asked questions

How do I write Big Intersection in LaTeX?

Type \bigcap in math mode, for example $\bigcap_{n=1}^{\infty} \left( 0, \frac{1}{n} \right) = \varnothing$. It works in plain LaTeX without loading any package.

Which package do I need for \bigcap?

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

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

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\bigcap$ 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).