Infinity in LaTeX

The infinity symbol ∞ is \infty in math mode: $x \to \infty$ . Put a minus sign in front for negative infinity (-\infty) and use it as a limit, bound or interval end like any other symbol.

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Infinity commands

\infty
$\infty$
Infinity ∞.
-\infty
$- \infty$
Negative infinity.
\pm\infty
$\pm \infty$
Plus or minus infinity.
(-\infty, \infty)
$(- \infty, \infty)$
The whole real line as an interval.
\aleph_0
$ℵ_{0}$
Aleph null, the cardinality of the natural numbers.
\lim_{x \to \infty}
$lim_{x \to \infty}$
Limit as x tends to infinity.

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LaTeX

Templates

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Infinity examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Limit at infinity
$lim_{x \to \infty} {(1 + \frac{1}{x})}^{x} = e$
LaTeX
```
\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x = e
```
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Infinite series
$\sum_{n = 1}^{\infty} \frac{1}{n^{2}} = \frac{π^{2}}{6}$
LaTeX
```
\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}
```
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Improper integral
$\int_{- \infty}^{\infty} e^{- x^{2}} d x = \sqrt{π}$
LaTeX
```
\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}
```
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Interval
$x \in (- \infty, 0] \cup [1, \infty)$
LaTeX
```
x \in (-\infty, 0] \cup [1, \infty)
```
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Divergence
$lim_{x \to 0^{+}} \frac{1}{x} = + \infty$
LaTeX
```
\lim_{x \to 0^+} \frac{1}{x} = +\infty
```
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Extended real line
$\overset{―}{R} = R \cup {- \infty, + \infty}$
LaTeX
```
\overline{\mathbb{R}} = \mathbb{R} \cup \{-\infty, +\infty\}
```
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Infinity as a limit or bound

Limits and bounds go in subscripts and superscripts: \lim_{n \to \infty}, \sum_{k=0}^{\infty}, \int_0^{\infty}. In displayed equations the bounds sit above and below the operator; inline they move to the side. Add \limits (\sum\limits_{k=0}^{\infty}) to force them above and below in a line of text.

Intervals are written with ordinary brackets: an open end at infinity uses a parenthesis, [0, \infty), because infinity is not a real number that the interval could include.

Infinity in text mode

\infty is a math symbol, so in a sentence write $\infty$ . With XeLaTeX or LuaLaTeX and a font that has it, you can also type ∞ directly.

Common mistakes

There is no \infinity or \infin command; LaTeX reports "Undefined control sequence".
Instead of
```
\infinity
```
Write
```
\infty
```
\inf exists but prints "inf", the infimum operator, not the ∞ symbol.
Instead of
```
\inf
```
Write
```
\infty
```
An interval of real numbers is open at infinity, so the bracket on that side is a parenthesis.
Instead of
```
[0, \infty]
```
Write
```
[0, \infty)
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\infty works in any document without packages; \aleph is built in as well.
MathJax and KaTeX
MathJax and KaTeX render \infty, \aleph_0 and the limit notation exactly as shown.
Microsoft Word
In a Word equation, type \infty and press Space for ∞. For limits and sums with infinity, build the formula here and use Copy for Word to paste an editable equation.