TeXipedia

nless

Represents the negation of the less-than relation, indicating that one value is not strictly less than another.

Overview

Serves as a fundamental symbol in mathematical logic, set theory, and formal proofs where precise inequality relationships need to be expressed.

  • Commonly used in advanced mathematics and theoretical computer science to denote counterexamples or exceptions.
  • Particularly useful in formal mathematical writing where standard keyboard symbols like '!<' would be inappropriate.
  • Often appears alongside other relation negation symbols in formal mathematical statements and proofs.
  • Provides a more elegant and typographically consistent alternative to combining negation with basic inequality symbols.

Examples

Expressing that one quantity is not less than another in a mathematical inequality.

x≮y  ⟹  x≥yx \nless y \implies x \geq y 
x \nless y \implies x \geq y

Comparing set cardinalities where one is not less than the other.

∣A∣≮∣B∣  ⟺  ∣A∣≥∣B∣|A| \nless |B| \iff |A| \geq |B| 
|A| \nless |B| \iff |A| \geq |B|

Showing the negation of a strict ordering relation in number theory.

For n∈N,n≮n\text{For } n \in \mathbb{N}, n \nless n 
\text{For } n \in \mathbb{N}, n \nless n