coloneqq

Represents a definition or assignment with a colon-equals symbol, commonly used in mathematical writing to indicate that a term is being defined.

Overview

Provides a more formal and semantically precise alternative to the simple equals sign when introducing mathematical definitions or declaring variables.

Widely used in theoretical mathematics and computer science to distinguish definitions from equations.
Particularly common in formal proofs, abstract algebra, and algorithm descriptions.
Helps readers quickly identify where new terms or concepts are being introduced in mathematical text.
Often preferred over := as it better matches traditional typographical conventions for mathematical writing.

Examples

Defining a mathematical sequence with proper definition notation.

a_n \coloneqq \frac{1}{n^2}

a_n \coloneqq \frac{1}{n^2}

Introducing a new variable in terms of existing expressions.

x \coloneqq 2y + z

x \coloneqq 2y + z

Defining a set using set-builder notation.

S \coloneqq \{x \in \mathbb{R} : x > 0\}

S \coloneqq \{x \in \mathbb{R} : x > 0\}