\coloneqq - LaTeX Symbol

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: =

\coloneqq

The symbol \coloneqq is used to denote a definition or an assignment in mathematical expressions. It is a relational operator that indicates that the expression on the left-hand side is defined to be equal to the expression on the right-hand side. This symbol is particularly useful in formal mathematical writing to clarify that a new term or notation is being introduced and defined.

Examples

a : = b + c

Defines 'a' as the sum of 'b' and 'c'.

a \coloneqq b + c

f (x) : = x^{2} + 2 x + 1

Defines the function f(x) as a quadratic expression.

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

S : = {x \in R ∣ x > 0}

Defines the set S as the set of all positive real numbers.

S \coloneqq \{ x \in \mathbb{R} \mid x > 0 \}