TeXipedia

varepsilon

Represents a variant form of the Greek letter epsilon, commonly used in mathematical notation and scientific equations.

Overview

Serves as an important mathematical symbol across multiple disciplines, particularly in analysis and physics where subtle distinctions between epsilon variants matter.

  • Often used to denote small positive quantities or error terms in mathematical proofs
  • Frequently appears in limit definitions and convergence criteria
  • Popular in optimization theory and numerical analysis
  • Distinguished from the standard epsilon (ε) by its more curved, lunate shape
  • Common in statistical notation for error terms or residuals

Examples

Defining a limit with a small positive value epsilon.

lim⁡ε→01ε=∞\lim_{\varepsilon \to 0} \frac{1}{\varepsilon} = \infty 
\lim_{\varepsilon \to 0} \frac{1}{\varepsilon} = \infty

Expressing an approximation within epsilon bounds.

∣f(x)−L∣<ε|f(x) - L| < \varepsilon 
|f(x) - L| < \varepsilon

Defining the error term in numerical analysis.

xn=x+εn, where ∣εn∣<10−6x_n = x + \varepsilon_n, \text{ where } |\varepsilon_n| < 10^{-6} 
x_n = x + \varepsilon_n, \text{ where } |\varepsilon_n| < 10^{-6}