How to create the empty set symbol in LaTeX?

# How to create the empty set symbol in LaTeX?

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This article aims to show you the simplest and easiest way to write the empty set symbol in LaTeX.

In mathematics for set theory the notation used is super important, that’s why today you will learn how to write the empty set symbol used in this area of math.

## Empty Set Symbol

This unique set is defined as a set that does not contain any element. Any set other than the empty set is called non-empty. Some textbooks refer to this set as the null set.

For example

## Empty Set Symbol in LaTeX

In LaTeX you have multiple options to insert this symbol in your document. One way is using the command \emptyset, it created a “0” (zero) with a slash in the middle, for example

\documentclass{article}
\begin{document}
$$A \cap B = \emptyset$$
\end{document}


Gives the output

Two sets do not have anything in common

Of course we are not limited to just this command to create this symbol, we have more commands that we can use.

## Empty Set Symbols Variation

The first variation in this article will be the notation ∅, inspired by the danish and norwegian alphabets. It does require the amssymb package, but does not need any argument. The command is \varnothing, as you can see it is slightly different from the others and is called the “null sign”.

For example

\documentclass{article}
\usepackage{amssymb}
\begin{document}
$$\forall A : A \cap \varnothing = \varnothing$$
\end{document}


Gives the output

The intersection of A with the empty set is the empty set

The second variation does not required packages, it is similar to the ∅ but is not the same symbol, the command is \O (big O vowel) inside math mode, the output looks more like a letter than a symbol, for example

\documentclass{article}
\begin{document}
$$\forall A : A \times \O = \O$$
\end{document}


Gives the output

Cartesian product of A and the empty set is the empty set

The third variation is another way to define the empty sets, it is represented by two curly brackets “{ }”. The commands for both curly brackets are \{ and \} respectively. It is recommended to use them inside math mode and alongside with the commands \left and \right. For example

\documentclass{article}
\begin{document}
$$B \cap C = \left \{ \right \}$$
\end{document}


There are multiple ways and commands to write the symbols for the empty set, only one requires a package, the other ones none. You decide which method works best for you.

I hope this article was helpful in guiding you in LaTeX, and as always keep writing in LaTeX.

All the images were created in LaTeX by the author. 