TeXipedia

curlyeqprec

Denotes a curly equals-precedes relation in mathematical notation, combining aspects of equality and precedence.

Overview

Serves as a specialized mathematical relation symbol primarily used in advanced algebra, order theory, and theoretical computer science where precise relationship notation is essential.

  • Common in formal proofs and mathematical logic where both equality and precedence need to be expressed simultaneously
  • Useful in describing partial orders, equivalence relations, and complex mathematical structures
  • Often appears alongside similar relation symbols in theoretical mathematics papers and textbooks

Examples

Defining a preorder relation in order theory using curly equals precedes.

x⋞y  ⟹  f(x)≤f(y)x \curlyeqprec y \implies f(x) \leq f(y) 
x \curlyeqprec y \implies f(x) \leq f(y)

Expressing a weak precedence relationship in a sequence analysis.

an⋞bn⋞cna_n \curlyeqprec b_n \curlyeqprec c_n 
a_n \curlyeqprec b_n \curlyeqprec c_n

Comparing convergence rates of sequences with curly equals precedes.

{xn}⋞{yn} as n→∞\{x_n\} \curlyeqprec \{y_n\} \text{ as } n \to \infty 
\{x_n\} \curlyeqprec \{y_n\} \text{ as } n \to \infty