TeXipedia

infin

Represents the mathematical concept of infinity, denoting unbounded or limitless quantities.

Overview

Essential in mathematical analysis, set theory, and various scientific fields where quantities approach unlimited values or processes continue without bound.

  • Commonly used in limit notation and series expansions
  • Appears frequently in calculus when discussing asymptotic behavior
  • Important in theoretical physics and computer science for describing algorithmic complexity
  • Used to denote infinite sets, sequences, and ranges in mathematical proofs

Examples

Expressing that a sequence approaches infinity.

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

Denoting an infinite interval in set notation.

(−∞,∞)(-\infin, \infin) 
(-\infin, \infin)

Indicating an improper integral to infinity.

∫0∞e−xdx=1\int_0^{\infin} e^{-x} dx = 1 
\int_0^{\infin} e^{-x} dx = 1