colonequals

Represents a definition or assignment using a colon followed by an equals sign, commonly used in mathematical and logical notation.

Overview

Serves as a formal notation to indicate that something is being defined, assigned a value, or declared equal by definition. This symbol combines the semantic meaning of both a colon and equals sign to create a more precise mathematical relationship.

Frequently used in formal mathematics and computer science to distinguish definitional equality from standard equality
Common in set theory and abstract algebra when introducing new terms or functions
Provides clearer notation than simple equals signs when establishing definitions or declaring new variables

Examples

Defining a mathematical sequence explicitly.

x_n \colonequals 2^n + 1

x_n \colonequals 2^n + 1

Introducing a new mathematical function definition.

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

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

Defining a set using set-builder notation.

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

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