Exists in LaTeX (\exists)

Where it is used

Gives the existential quantifier ∃, read "there exists" or "for some".

\exists asserts that at least one element satisfies a property, as in \exists x \in \mathbb{R} : x^2 = 2. Uniqueness is written \exists! (there exists exactly one), and \nexists gives the negated symbol for "there does not exist". Like \forall it is an ordinary symbol, so insert a thin space or a colon after the bound variable for readability. Quantifier order matters: \forall x\, \exists y differs from \exists y\, \forall x, so keep them in the intended sequence. In formal logic writing, parentheses around the scope, \exists x\,(P(x)), avoid ambiguity.

Also listed under: Logic & Proofs, Quantifiers

Minimal compilable example

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

\documentclass{article}
\usepackage{amssymb}
\begin{document}
Exists: $\exists$

\[ \exists!\, x \in \mathbb{R} : x^3 = 8 \]
\end{document}

Related symbols

• Element Of\in
• For All\forall
• Not Element Of\notin
• If and Only If\iff
• Subset\subset
• Implies\implies

Frequently asked questions

How do I write Exists in LaTeX?

Type \exists in math mode, for example $\exists!\, x \in \mathbb{R} : x^3 = 8$. It works in plain LaTeX without loading any package.

Which package do I need for \exists?

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

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

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