How to Write Infinity Symbol (∞) in LaTeX

August 04, 2023

To write infinity symbol (∞) in LaTeX document, use the LaTeX command \infty, it will add symbol ∞ in the text.

The infinity symbol (∞) is used to represent concepts related to infinity and unbounded quantities. It is widely used in calculus, set theory, complex analysis.

In this article, we will discuss how to type infinity symbol (∞) in the LaTeX document and their significance in the mathematical expressions, calculus and many other mathematical fields.

Symbol Overview

Symbol: Infinity Symbol

Unicode: U+221E

Type: Mathematical

Package Requirement: None (built-in symbol)

Argument: None (no additional arguments needed)

LaTeX Command: \infty

Example: ∞

Syntax

To use the infinity symbol (∞) in LaTeX, you can use the \infty command as given below.

\infty

Examples of Writing the Infinity Symbol

Let’s explore the some practical examples of using the LaTeX command to write the infinity symbol in document.

Write Infinity Symbol in Mathematical Expression

\documentclass{article}
\begin{document}
The limit of \(x\) as \(x\) approaches infinity is denoted as \(x \to \infty\).
\end{document}

Output: 👇️

The limit of x as x approaches infinity is denoted as x → ∞.

Here, in the above example, we use the infinity symbol to represent the concepts of approaching infinity value, as x goes to infinity.

Using Infinity Symbol in Calculus

\documentclass{article}
\begin{document}
\[\lim_{x \to \infty} f(x) = L \]
\end{document}

Output: 👇️

lim f(x) = L x→∞

In the above example of calculus, the infinity symbol is used to express a limit as a variable approaches infinity. It express the limit of function f(x) as x approaches infinity,and it equals to L.

Using Infinity Symbol in Set Theory

\documentclass{article}
\begin{document}
$A = \{x \mid x > 0, x \leq \infty\}$
\end{document}

Output: 👇️

A = {x | x > 0, x ≤ ∞}

Here, in the above example of set theory, the infinity symbol denotes an unbounded set. In this example, we define set A to include all positive real numbers greater than 0 and up to infinity (∞)

Using the Infinity Symbol in Real Analysis

\documentclass{article}
\begin{document}
\[\sum_{n=1}^{\infty} a_n\]
\end{document}

Output: 👇️ ∞ ∑a_n n=1

In the above example of Real analysis, the infinity symbol (∞) is used to represent an infinite series. In this example,we have an infinite sum of terms a_n from n = 1 to infinity.

Using the Infinity Symbol in Complex Analysis

\documentclass{article}
\begin{document}
$f(z) = \frac{1}{z}, \quad z \neq 0; \quad f(0) = \infty$
\end{document}

Output: 👇️

f (z) = 1/z , z ̸ = 0; f (0) = ∞

In complex analysis, the infinity symbol is used to represent points at infinity on the Riemann sphere. In this example, we define a complex function f(z) where z is not equal to 0, and f(0) is considered to be infinity.

Conclusion

The infinity symbol (∞) in LaTeX is a powerful notation to represent concepts related to infinity, limitless values, approaching infinity.

It is widely used in calculus, mathematical expressions, set theory, real analysis and many other mathematical fields.

Write writing the infinity symbol in LaTeX documents, ensure appropriate spacing around the infinity symbol in text for readability.