Empty Set in LaTeX (\emptyset)

Where it is used

Denotes the empty set, the unique set that contains no elements at all.

\emptyset prints the default empty-set glyph, a circle with a slash. Many mathematicians prefer the rounder form \varnothing, which is distinct from a zero with a slash and is common in modern texts. Choose one and use it consistently. Typical uses are disjointness A \cap B = \emptyset and set builder results. Do not confuse it with the Scandinavian letter Ø or with \phi and \varphi. Writing \{\} for the empty set is also acceptable, but note that \{\emptyset\} is a set with one element.

Also listed under: Set Theory

Minimal compilable example

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

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Empty Set: $\emptyset$

\[ A \cap B = \emptyset \implies P(A \cup B) = P(A) + P(B) \]
\end{document}

Related symbols

• Partial Derivative\partial
• Intersection\cap
• Nabla\nabla
• Union\cup
• Plus Minus\pm
• Subset\subset

Frequently asked questions

How do I write Empty Set in LaTeX?

Type \emptyset in math mode, for example $A \cap B = \emptyset \implies P(A \cup B) = P(A) + P(B)$. It works in plain LaTeX without loading any package.

Which package do I need for \emptyset?

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

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

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