Eqqcolon

Represents a colon-based definition relationship where the left side is being defined in terms of the right side, commonly used in mathematical proofs and formal definitions.

Overview

Serves as a specialized mathematical notation indicating definitional equality, with the colon positioned on the right side of the equals sign to show that the left-hand expression is being defined.

Particularly useful in formal mathematics and theoretical computer science for introducing new notation or concepts.
Often employed when establishing mathematical definitions, theorems, or formal specifications.
Provides clearer visual distinction than standard equals signs when explicitly defining new terms or expressions.
Part of a family of definition symbols that includes := and =:, offering precise control over definition directionality.

Examples

Defining a mathematical sequence explicitly.

x_n \Eqqcolon \frac{1}{n^2} \quad \text{for } n \geq 1

x_n \Eqqcolon \frac{1}{n^2} \quad \text{for } n \geq 1

Introducing a new mathematical operator.

f \diamond g \Eqqcolon f(g(x))

f \diamond g \Eqqcolon f(g(x))

Defining a set with specific properties.

S \Eqqcolon \{x \in \mathbb{R} : x^2 < 4\}

S \Eqqcolon \{x \in \mathbb{R} : x^2 < 4\}