eqqcolon

Represents a colon-based equality symbol that places the colon on the right side of the equals sign, commonly used in mathematical definitions and formal proofs.

Overview

Provides a visually clear way to introduce mathematical definitions or establish equivalences where the defined term appears on the right side of the expression. Part of a family of definition symbols that includes \coloneqq and related variants.

Frequently used in formal mathematics and theoretical computer science
Particularly useful when defining variables, functions, or sets where the defined term follows the definition
Helps maintain consistent notation in mathematical writing where the direction of definition needs to be explicitly indicated

Examples

Defining a mathematical sequence using the equals-with-colon notation.

x_n \eqqcolon \frac{1}{n^2}

x_n \eqqcolon \frac{1}{n^2}

Introducing a new mathematical function with explicit definition.

f(x) \eqqcolon x^2 + 2x + 1

f(x) \eqqcolon x^2 + 2x + 1

Defining a set using explicit construction.

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

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