TeXipedia

ne

Represents mathematical inequality, indicating that two values or expressions are not equal to each other.

Overview

Essential for mathematical notation across many fields where distinguishing between unequal quantities is necessary.

  • Commonly used in algebra and logic to express inequalities and constraints
  • Appears frequently in computer science for conditional statements and set theory
  • More formal alternative to the informal not-equals notation (=/=)
  • Often used in mathematical proofs and theorem statements where precise notation is required

Examples

Expressing inequality in a mathematical statement

x≠y  ⟹  x2≠y2x \ne y \implies x^2 \ne y^2 
x \ne y \implies x^2 \ne y^2

Defining a set by excluding a specific value

{x∈R:x≠0}\{x \in \mathbb{R} : x \ne 0\} 
\{x \in \mathbb{R} : x \ne 0\}

Expressing a condition in a limit calculation

lim⁡x→1,x≠1x2−1x−1\lim_{x \to 1, x \ne 1} \frac{x^2 - 1}{x - 1} 
\lim_{x \to 1, x \ne 1} \frac{x^2 - 1}{x - 1}