TeXipedia

doteq

Represents a relation indicating equality with a dot above the equals sign, commonly used to denote definitions or special forms of equality.

Overview

Primarily used in mathematical notation where a distinct form of equality needs to be emphasized or when defining new terms and expressions.

  • Common in abstract algebra and theoretical mathematics to indicate definitions or specialized equality relations.
  • Often appears in proofs and formal mathematical writing to distinguish from standard equality.
  • Useful when showing that expressions are equal by definition rather than through mathematical manipulation.
  • Frequently encountered in textbooks and academic papers where precise mathematical notation is essential.

Examples

Defining a sequence where each term equals its predecessor plus a constant.

an+1≐an+ca_{n+1} \doteq a_n + c 
a_{n+1} \doteq a_n + c

Showing approximate equality in a differential equation.

dydx≐y+x\frac{dy}{dx} \doteq y + x 
\frac{dy}{dx} \doteq y + x

Indicating equality by definition in a vector space.

v⃗≐(x1,x2,…,xn)\vec{v} \doteq (x_1, x_2, \ldots, x_n) 
\vec{v} \doteq (x_1, x_2, \ldots, x_n)