Infinity (∞) in LaTeX
\infty produces the infinity symbol, most often as a limit of integration, the target of a limit, or an index bound.
LaTeX command
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The command \infty renders the lemniscate (sideways figure-eight). It appears as an integral bound (\int_0^\infty), the target of a limit (\lim_{x \to \infty}) and the upper limit of an infinite series (\sum_{n=1}^\infty). Use \to inside a limit to say the variable tends to infinity.
For signed infinities prefix the symbol: -\infty for negative infinity and \pm\infty for plus-or-minus infinity. It also forms unbounded intervals, as in (-\infty, \infty) for the whole real line, or [0, \infty) for the non-negative reals.
\infty is an ordinary symbol, not an operator, and needs no package. When it is part of a longer sub- or superscript, brace it: \int_{-\infty}^{\infty} and \sum_{n=1}^{\infty}. Bear in mind infinity is not a number, so expressions like \infty - \infty do not simplify.
Examples
$\lim_{x \to \infty} \frac{1}{x} = 0$a limit at infinity
$\int_0^{\infty} e^{-x}\,dx = 1$an improper integral
$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$an infinite series
$(-\infty, \infty)$the whole real line as an interval
$x \to -\infty$tending to negative infinity
Tips and common mistakes
\inftyis a single ordinary symbol; write -\inftyor\pm\inftyfor signed infinities.- In a limit use
\to:\lim_{x \to \infty}; the subscript stacks under 'lim' in display mode. - Brace it inside longer bounds:
\int_{-\infty}^{\infty}and\sum_{n=1}^{\infty}. - Infinity is not a number; avoid writing
\infty-\inftyas if it simplified.
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What is the LaTeX command for infinity?
\infty in math mode. No package is required.
How do I write negative infinity or plus/minus infinity?
Prefix the symbol: -\infty for negative infinity and \pm\infty for plus-or-minus infinity.
How do I use infinity as an integral or limit bound?
Place it in the superscript or subscript, e.g. \int_0^{\infty} f(x)\,dx or \lim_{n \to \infty} a_n; brace it when it is part of a longer expression.