Not Exists in LaTeX (\nexists)

Where it is used

Negated existential quantifier: there does not exist an object with the stated property.

\nexists x \in \mathbb{Q} : x^2 = 2 states that 2 has no rational square root. The glyph is a slashed \exists designed as a single glyph; \not\exists also works but the slash may be misplaced. Logically it is equivalent to \forall x\, \neg P(x), and many logicians prefer writing \neg \exists x for clarity. Add a small space or a colon after the bound variable, as in \nexists x \, P(x). For unique existence the symbol is \exists!.

Also listed under: 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}
Not Exists: $\nexists$

\[ \nexists\, x \in \mathbb{Q} : x^2 = 2 \]
\end{document}

Related symbols

• Negation\neg
• Exists\exists
• Logical And\land
• For All\forall
• Logical Or\lor
• Right Arrow (Double)\Rightarrow

Frequently asked questions

How do I write Not Exists in LaTeX?

Type \nexists in math mode, for example $\nexists\, x \in \mathbb{Q} : x^2 = 2$. Load amssymb first with \usepackage{amssymb}.

Which package do I need for \nexists?

\nexists needs amssymb: add \usepackage{amssymb} to your preamble before the document starts.

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

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