TeXipedia

Doteq

Represents a relation indicating equality with a dot above the equals sign, commonly used in mathematical proofs and definitions.

Overview

Serves as a specialized equality symbol in mathematical notation, particularly useful when defining new terms or showing equivalence with additional emphasis.

  • Often appears in formal mathematical writing to introduce definitions
  • Used in abstract algebra and theoretical mathematics to distinguish special forms of equality
  • Helpful in contexts where regular equality needs visual distinction
  • Common in proof-writing where step-by-step reasoning requires clear notation differentiation

Examples

Defining a relation that is both equal and derivative.

f(x)≑g(x)  ⟹  f′(x)=g′(x)f(x) \Doteq g(x) \implies f'(x) = g'(x) 
f(x) \Doteq g(x) \implies f'(x) = g'(x)

Indicating equality up to normalization in quantum mechanics.

∣ψ⟩≑1N∣ϕ⟩|\psi\rangle \Doteq \frac{1}{\sqrt{N}} |\phi\rangle 
|\psi\rangle \Doteq \frac{1}{\sqrt{N}} |\phi\rangle

Denoting equivalence of sequences up to a constant factor.

{an}≑{bn} as n→∞\{a_n\} \Doteq \{b_n\} \text{ as } n \to \infty 
\{a_n\} \Doteq \{b_n\} \text{ as } n \to \infty