TeXipedia

gtreqqless

Represents a combination of greater than, equal to, and less than relations in mathematical expressions where multiple comparisons are needed.

Overview

Serves as a specialized relational operator in advanced mathematical notation, particularly useful in formal mathematical proofs and complex inequality statements.

  • Common in abstract algebra and analysis when describing relationships between multiple quantities
  • Used when expressing transitional or uncertain relationships between mathematical expressions
  • Helpful in scenarios where the relationship between quantities may vary under different conditions
  • Often appears in mathematical logic and set theory contexts

Examples

Comparing two sequences in number theory.

{an}⪌{bn} as n→∞\{a_n\} \gtreqqless \{b_n\} \text{ as } n \to \infty 
\{a_n\} \gtreqqless \{b_n\} \text{ as } n \to \infty

Expressing uncertainty in a numerical analysis inequality.

f(x)⪌g(x) for x∈(0,1)f(x) \gtreqqless g(x) \text{ for } x \in (0,1) 
f(x) \gtreqqless g(x) \text{ for } x \in (0,1)

Comparing statistical estimators with ambiguous relative efficiency.

θ^1⪌θ^2\hat{\theta}_1 \gtreqqless \hat{\theta}_2 
\hat{\theta}_1 \gtreqqless \hat{\theta}_2