For All in LaTeX (\forall)

Where it is used

Gives the universal quantifier ∀, read "for all" or "for every".

\forall begins universally quantified statements, as in the epsilon-delta definition \forall \varepsilon > 0\ \exists \delta > 0. TeX treats it as an ordinary symbol, so there is no automatic space after the bound variable; add \, or \ or a separator like a colon or period depending on your convention. In prose-heavy proofs, many style guides prefer writing "for all" in words rather than \forall. In typed lambda calculus and type theory it also introduces polymorphic types, for example \forall \alpha.\, \alpha \to \alpha.

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}
\begin{document}
For All: $\forall$

\[ \forall \varepsilon > 0\ \exists \delta > 0 : |x - a| < \delta \]
\end{document}

Related symbols

• Exists\exists
• If and Only If\iff
• Element Of\in
• Implies\implies
• Not Element Of\notin
• Greater Than or Equal\geq

Frequently asked questions

How do I write For All in LaTeX?

Type \forall in math mode, for example $\forall \varepsilon > 0\ \exists \delta > 0 : |x - a| < \delta$. It works in plain LaTeX without loading any package.

Which package do I need for \forall?

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

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

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