Coloneq

Represents a colon-equals relation symbol commonly used in mathematical definitions and assignments.

Overview

Serves as a specialized mathematical operator that combines both equality and definition semantics, particularly useful in formal mathematics and computer science contexts.

Frequently appears in formal mathematical proofs and definitions
Used to denote formal definitions or assignments in mathematical writing
Common in theoretical computer science for specifying algorithms and definitions
Provides a more formal alternative to the standard equals sign when defining new concepts or variables

Examples

Defining a function using the colonequals symbol in mathematical notation.

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

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

Specifying a sequence definition with the colonequals symbol.

a_n \Coloneq 2^n - 1

a_n \Coloneq 2^n - 1

Defining a set using the colonequals notation.

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

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