TeXipedia

lneqq

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

Overview

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

  • Frequently appears in analysis and set theory to denote strict ordering relationships
  • Often used alongside other inequality symbols to express precise mathematical conditions
  • Particularly valuable in contexts where distinguishing between different types of inequalities is crucial
  • Common in academic papers and advanced mathematical texts where precise notation is essential

Examples

Comparing two real numbers where one is strictly less than but not equal to the other.

x≨y  ⟹  x<y and x≠yx \lneqq y \implies x < y \text{ and } x \neq y 
x \lneqq y \implies x < y \text{ and } x \neq y

Demonstrating strict inequality between functions.

f(x)≨g(x) for all x∈Rf(x) \lneqq g(x) \text{ for all } x \in \mathbb{R} 
f(x) \lneqq g(x) \text{ for all } x \in \mathbb{R}

Showing strict ordering in a sequence convergence.

an≨L for all n∈Na_n \lneqq L \text{ for all } n \in \mathbb{N} 
a_n \lneqq L \text{ for all } n \in \mathbb{N}