triangleq

Denotes a triangular equals symbol used to indicate definitions or definitional equality in mathematical writing.

Overview

Commonly employed in formal mathematics and theoretical computer science to explicitly distinguish definitional equality from standard equality relationships.

Particularly useful in abstract algebra and formal logic when introducing new terms or concepts.
Provides a visually distinct alternative to := notation.
Often appears in academic papers and textbooks where precise mathematical notation is essential.
Helps readers quickly identify where new mathematical objects or relationships are being defined.

Examples

Defining a new mathematical operator or function.

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

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

Introducing a sequence definition in number theory.

a_n \triangleq 2^n - 1

a_n \triangleq 2^n - 1

Defining a set in mathematical notation.

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

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