TeXipedia

eqslantgtr

Represents a slanted greater-than-or-equal-to relationship, combining the concepts of inequality and equivalence in mathematical expressions.

Overview

Serves as a specialized mathematical comparison operator primarily used in advanced algebra, analysis, and theoretical mathematics where precise relationship notation is crucial.

  • Common in formal mathematical proofs and theoretical computer science
  • Used to denote ordered relationships that are both greater than and approximately equal
  • Particularly useful in contexts involving asymptotic behavior and order relations
  • Often appears alongside other specialized comparison operators in complex mathematical arguments

Examples

Comparing growth rates of functions in asymptotic analysis.

f(n)⪖n2 as n→∞f(n) \eqslantgtr n^2 \text{ as } n \to \infty 
f(n) \eqslantgtr n^2 \text{ as } n \to \infty

Expressing strict dominance in game theory payoffs.

u1(s1)⪖u1(s2)u_1(s_1) \eqslantgtr u_1(s_2) 
u_1(s_1) \eqslantgtr u_1(s_2)

Showing proper containment in set theory with additional emphasis.

A⪖B  ⟹  ∣A∣>∣B∣A \eqslantgtr B \implies |A| > |B| 
A \eqslantgtr B \implies |A| > |B|