TeXipedia

not

Creates a negation by drawing a diagonal line through the following symbol or relation.

Overview

Essential for expressing mathematical negations and inequalities in formal logic, set theory, and general mathematics.

  • Commonly used with equality (≠), subset (⊄), and other relation symbols.
  • Particularly important in logical proofs and mathematical statements.
  • Provides a more compact alternative to writing "not" in mathematical expressions.
  • Frequently appears in abstract algebra, formal logic, and computer science notation.

Examples

Expressing that two values are not equal in a mathematical equation

x≠y  ⟹  ∣x−y∣>0x \not = y \implies |x-y| > 0 
x \not = y \implies |x-y| > 0

Showing non-divisibility in number theory

p∤nmeans p does not divide np \not | n \quad \text{means } p \text{ does not divide } n 
p \not | n \quad \text{means } p \text{ does not divide } n

Expressing that a number is not less than another in an inequality

x≮y  ⟹  x≥yx \not < y \implies x \geq y 
x \not < y \implies x \geq y