TeXipedia

doteqdot

Represents a mathematical relation showing equality with three dots, combining both above and below the equals sign.

Overview

Primarily used in advanced mathematical notation to indicate a special form of equality or equivalence relationship, particularly in abstract algebra and theoretical mathematics.

  • Common in proofs and formal mathematical writing where precise relationship distinctions are crucial.
  • Often appears in contexts involving sequence equivalences or specialized algebraic relations.
  • Serves as a more elaborate variant of the dotted equals sign, providing additional emphasis or specific mathematical meaning depending on the context.

Examples

Expressing a relation between sequences that are equal both term-by-term and in their limits.

{an}≑{bn}  ⟹  lim⁡n→∞an=lim⁡n→∞bn\{a_n\} \doteqdot \{b_n\} \implies \lim_{n \to \infty} a_n = \lim_{n \to \infty} b_n 
\{a_n\} \doteqdot \{b_n\} \implies \lim_{n \to \infty} a_n = \lim_{n \to \infty} b_n

Showing equivalence between two expressions in a mathematical proof.

f(x)+c≑g(x)+cf(x) + c \doteqdot g(x) + c 
f(x) + c \doteqdot g(x) + c

Indicating equality of derivatives and function values at a point.

f(x)≑g(x) at x=af(x) \doteqdot g(x) \text{ at } x = a 
f(x) \doteqdot g(x) \text{ at } x = a