TeXipedia

infty

Represents the mathematical concept of infinity, used to denote unbounded quantities or limits that grow without bound.

Overview

Essential in mathematical notation across numerous fields, particularly when discussing limits, series, and infinite quantities.

  • Commonly used in calculus when describing limits approaching infinity
  • Appears frequently in set theory to describe infinite sets
  • Important in analysis for discussing asymptotic behavior
  • Used in physics and engineering to represent theoretical bounds or ideal cases
  • Often paired with summation or integral notation to indicate infinite bounds

Examples

Expressing the limit of a sequence approaching infinity

lim⁡n→∞1n=0\lim_{n \to \infty} \frac{1}{n} = 0 
\lim_{n \to \infty} \frac{1}{n} = 0

Denoting an infinite interval in set notation

(−∞,∞)(-\infty, \infty) 
(-\infty, \infty)

Representing an infinite series

∑n=1∞1n2=π26\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} 
\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}