TeXipedia

nleqq

Represents a negated double less-than-or-equal-to relationship, indicating that one value is not less than or equal to another with an emphasized inequality.

Overview

Serves as a specialized negation operator in mathematical proofs and formal logic where precise inequality relationships need to be expressed.

  • Common in advanced algebra and analysis for expressing strict ordering relationships
  • Used in formal mathematical writing to denote non-subset relationships in set theory
  • Particularly useful in contexts where standard inequalities need explicit negation
  • Often appears in theoretical computer science and mathematical logic for expressing constraints and conditions

Examples

Expressing a strict inequality between sequences or series.

{an}≰{bn} for all n≥N\{a_n\} \nleqq \{b_n\} \text{ for all } n \geq N 
\{a_n\} \nleqq \{b_n\} \text{ for all } n \geq N

Comparing functions with strict inequality over an interval.

f(x)≰g(x) on [a,b]f(x) \nleqq g(x) \text{ on } [a,b] 
f(x) \nleqq g(x) \text{ on } [a,b]

Showing non-dominance in partial ordering of sets.

A≰B  ⟹  ∃x∈A:x∉BA \nleqq B \implies \exists x \in A: x \not\in B 
A \nleqq B \implies \exists x \in A: x \not\in B