TeXipedia

nleqslant

Represents a negated less-than-or-equal-to relationship with a slanted line through it, commonly used in mathematical inequalities.

Overview

Essential for expressing complex mathematical relationships where one quantity is specifically not less than or equal to another, appearing frequently in advanced mathematics and formal proofs.

  • Common in abstract algebra and analysis for expressing strict inequalities
  • Used when defining boundary conditions or constraints in mathematical optimization
  • Particularly useful in formal mathematical writing where precise negation of inequalities is required
  • Often appears alongside other inequality symbols in systems of equations or logical statements

Examples

Expressing a strict inequality between sequences.

{an}≰{bn} for some n∈N\{a_n\} \nleqslant \{b_n\} \text{ for some } n \in \mathbb{N} 
\{a_n\} \nleqslant \{b_n\} \text{ for some } n \in \mathbb{N}

Showing a counterexample in real analysis.

x≰y  ⟹  x>yx \nleqslant y \implies x > y 
x \nleqslant y \implies x > y

Comparing function values in analysis.

f(x)≰M at x=x0f(x) \nleqslant M \text{ at } x = x_0 
f(x) \nleqslant M \text{ at } x = x_0