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succeq

Represents a binary relation meaning 'greater than or equal to' with a curvy bottom, commonly used in mathematical proofs and set theory.

Overview

Serves as a specialized comparison operator in mathematical contexts where a more formal or precise notation than the standard ≥ is desired.

  • Frequently appears in order theory and abstract algebra to denote partial ordering relationships
  • Common in academic papers and advanced mathematical texts when discussing ordered sets
  • Often used alongside its companion symbol \preceq to establish formal inequalities
  • Particularly useful in contexts involving optimization theory and mathematical analysis where precise relation notation is essential

Examples

Defining a partial order relation on a set of real numbers.

x⪰y  ⟺  x−y≥0x \succeq y \iff x - y \geq 0 
x \succeq y \iff x - y \geq 0

Expressing preference relations in economics.

A⪰B⪰CA \succeq B \succeq C 
A \succeq B \succeq C

Comparing matrices in terms of their eigenvalues.

M1⪰M2 if λ1≥λ2M_1 \succeq M_2 \text{ if } \lambda_1 \geq \lambda_2 
M_1 \succeq M_2 \text{ if } \lambda_1 \geq \lambda_2