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nleq

Represents the mathematical relation 'not less than or equal to' in formal expressions and proofs.

Overview

Essential for expressing strict inequalities and negated relations in mathematical logic, set theory, and formal proofs.

  • Commonly used in advanced mathematics to explicitly state when one quantity is not less than or equal to another
  • Appears frequently in analysis, abstract algebra, and theoretical computer science
  • Particularly useful when proving statements by contradiction or when precise logical negation is required
  • Often paired with other inequality symbols in complex mathematical expressions

Examples

Expressing a strict upper bound in an inequality.

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

Showing a counterexample in number theory.

2n≰n2 for n≥52^n \nleq n^2 \text{ for } n \geq 5 
2^n \nleq n^2 \text{ for } n \geq 5

Comparing sequence terms in analysis.

{an} diverges since an+1≰an\{a_n\} \text{ diverges since } a_{n+1} \nleq a_n 
\{a_n\} \text{ diverges since } a_{n+1} \nleq a_n