Empty Set in LaTeX

LaTeX has two empty set symbols: \emptyset (built in, a slashed zero shape) and \varnothing (amssymb, a round circle with a slash, the form most textbooks print). Both are math-mode commands: $A \cap B = \varnothing$ .

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Empty set commands

\emptyset
$\emptyset$
Empty set, built into LaTeX.
\varnothing
$\emptyset$
Rounder empty set; needs \usepackage{amssymb}.
\{\}
${}$
Empty braces: the empty set written as a set with no elements.
\{ \varnothing \}
${\emptyset}$
The set containing the empty set (not empty!).
\mathcal{P}(\varnothing)
$P (\emptyset)$
Power set of the empty set.

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LaTeX

Templates

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Empty set examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Disjoint sets
$A \cap B = \emptyset$
LaTeX
```
A \cap B = \varnothing
```
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Empty solution set
${x \in R : x^{2} = - 1} = \emptyset$
LaTeX
```
\{ x \in \mathbb{R} : x^2 = -1 \} = \emptyset
```
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Subset of every set
$\emptyset \subseteq A for every set A$
LaTeX
```
\varnothing \subseteq A \quad \text{for every set } A
```
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Not empty
$S \neq \emptyset$
LaTeX
```
S \neq \varnothing
```
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Power set
$P (\emptyset) = {\emptyset}$
LaTeX
```
\mathcal{P}(\varnothing) = \{ \varnothing \}
```
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Both symbols side by side
$\emptyset vs \emptyset$
LaTeX
```
\emptyset \quad \text{vs} \quad \varnothing
```
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\emptyset or \varnothing?

They mean the same thing; the difference is only the shape. \emptyset in the default Computer Modern font is a tall, narrow slashed zero. \varnothing is a round circle with a slash, which is what most printed math books use and what many people expect ∅ to look like.

To use the round form everywhere without changing your source, redefine the command once in the preamble after loading amssymb.

LaTeX

\usepackage{amssymb}
\let\emptyset\varnothing

Writing an empty set with braces

Braces group things in LaTeX, so {} prints nothing. To show the braces themselves, escape them: \{\}. The same applies to any set written out, such as \{1, 2, 3\}.

Common mistakes

\O is the Scandinavian letter Ø in text mode. It resembles the symbol but is a letter, and it is not valid in math mode.
Instead of
```
A \cap B = \O
```
Write
```
A \cap B = \varnothing
```
\varnothing comes from amssymb; without it LaTeX reports "Undefined control sequence".
Instead of
```
\varnothing  % no amssymb
```
Write
```
\usepackage{amssymb}
```
Unescaped braces are grouping characters and disappear from the output.
Instead of
```
A = {}
```
Write
```
A = \{\}
```
φ is the Greek letter phi. It looks similar in handwriting but is a different symbol.
Instead of
```
\phi  % as the empty set
```
Write
```
\varnothing
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\emptyset works in any document; \varnothing needs \usepackage{amssymb}.
MathJax and KaTeX
MathJax and KaTeX support both \emptyset and \varnothing with no setup; the two shapes differ there as well.
Microsoft Word
In a Word equation, \emptyset followed by Space inserts ∅. Copy for Word from the editor here pastes set formulas as editable equations.