Infinity in LaTeX (\infty)

Where it is used

Draws the lemniscate ∞, representing an unbounded quantity or a limit that grows without bound.

You will see \infty in limits like x \to \infty, improper integrals \int_0^\infty e^{-x}\,dx, and series bounds \sum_{n=1}^{\infty}. It also names the sup norm \|f\|_\infty, the space L^\infty, and smooth functions C^\infty. Write -\infty and +\infty with the sign attached; TeX spaces the sign correctly as unary. Remember that \infty is not a real number, so an interval containing it should be open at that end, as in [0, \infty). For the extended reals, \overline{\mathbb{R}} is a common notation.

Also listed under: Calculus & Analysis

Minimal compilable example

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

\documentclass{article}
\begin{document}
Infinity: $\infty$

\[ \int_{0}^{\infty} e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2} \]
\end{document}

Related symbols

• Approximately Equal\approx
• Limit\lim_{x \to \infty}
• Not Equal\neq
• Integral\int_{a}^{b}
• Less Than or Equal\leq
• Product\prod_{i=1}^{n}

Frequently asked questions

How do I write Infinity in LaTeX?

Type \infty in math mode, for example $\int_{0}^{\infty} e^{-x^2}\,dx = \frac{\sqrt{\pi}}{2}$. It works in plain LaTeX without loading any package.

Which package do I need for \infty?

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

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

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