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gneqq

Represents a strict greater-than relationship with an additional line indicating non-equality, commonly used in mathematical proofs and set theory.

Overview

Serves as a specialized relational operator in advanced mathematics, particularly useful when emphasizing strict inequality relationships.

  • Frequently appears in formal mathematical writing where precise distinctions between inequalities are crucial.
  • Common in set theory, analysis, and abstract algebra when standard inequality symbols are insufficient.
  • Provides a visually distinct alternative to the regular greater-than symbol, helping readers quickly identify non-equality conditions.
  • Often used alongside similar symbols like \leqq and \geqq in mathematical arguments and proofs.

Examples

Comparing two sequences that are strictly decreasing.

an≩an+1for all n∈Na_n \gneqq a_{n+1} \quad \text{for all } n \in \mathbb{N} 
a_n \gneqq a_{n+1} \quad \text{for all } n \in \mathbb{N}

Expressing a strict inequality between sets.

A≩B  ⟹  ∣A∣>∣B∣A \gneqq B \implies |A| > |B| 
A \gneqq B \implies |A| > |B|

Showing strict inequality in analysis.

f(x)≩g(x) on [a,b]f(x) \gneqq g(x) \text{ on } [a,b] 
f(x) \gneqq g(x) \text{ on } [a,b]