TeXipedia

neq

Represents inequality or non-equivalence between mathematical expressions, indicating that two values or expressions are not equal.

Overview

Essential for mathematical notation across various disciplines where distinguishing between unequal quantities is necessary.

  • Commonly used in algebra and logic to express non-equality conditions
  • Appears frequently in computer science for conditional statements and boolean logic
  • Important in mathematical proofs and theorem statements where exclusion cases need to be specified
  • Often used alongside other comparison operators in systems of equations or inequalities

Examples

Expressing that two expressions are not equal in a mathematical statement.

x+2≠x−2x + 2 \neq x - 2 
x + 2 \neq x - 2

Showing a contradiction in a mathematical proof by contradiction.

If n is even, then n2≠2k+1\text{If } n \text{ is even, then } n^2 \neq 2k + 1 
\text{If } n \text{ is even, then } n^2 \neq 2k + 1

Comparing sets in set theory.

A∩B≠∅A \cap B \neq \emptyset 
A \cap B \neq \emptyset