TeXipedia

succcurlyeq

Denotes a curly greater-than-or-equal-to relationship with succession, commonly used in mathematical ordering and set theory.

Overview

Represents a specialized ordering relation that combines the concepts of succession and inequality, particularly useful in advanced mathematics and formal logic.

  • Frequently appears in order theory and abstract algebra
  • Used to express refined comparisons where standard inequality symbols are insufficient
  • Common in proofs and theoretical mathematics where precise ordering relationships need to be distinguished
  • Often employed alongside other related ordering symbols to establish complex mathematical hierarchies

Examples

Expressing a strictly increasing sequence that is also greater than or equal to a value.

an≽0 for all n∈Na_n \succcurlyeq 0 \text{ for all } n \in \mathbb{N} 
a_n \succcurlyeq 0 \text{ for all } n \in \mathbb{N}

Comparing sequences in analysis with strict succession and inequality.

{xn}≽{yn}  ⟹  lim⁡n→∞xn>lim⁡n→∞yn\{x_n\} \succcurlyeq \{y_n\} \implies \lim_{n \to \infty} x_n > \lim_{n \to \infty} y_n 
\{x_n\} \succcurlyeq \{y_n\} \implies \lim_{n \to \infty} x_n > \lim_{n \to \infty} y_n

Defining order relations in partially ordered sets.

x≽y  ⟺  (x>y or x=y)x \succcurlyeq y \iff (x > y \text{ or } x = y) 
x \succcurlyeq y \iff (x > y \text{ or } x = y)