doteq
Represents a relation indicating equality with a dot above the equals sign, commonly used to denote definitions or special forms of equality.
Overview
Primarily used in mathematical notation where a distinct form of equality needs to be emphasized or when defining new terms and expressions.
- Common in abstract algebra and theoretical mathematics to indicate definitions or specialized equality relations.
- Often appears in proofs and formal mathematical writing to distinguish from standard equality.
- Useful when showing that expressions are equal by definition rather than through mathematical manipulation.
- Frequently encountered in textbooks and academic papers where precise mathematical notation is essential.
Examples
Defining a sequence where each term equals its predecessor plus a constant.
a_{n+1} \doteq a_n + c
Showing approximate equality in a differential equation.
\frac{dy}{dx} \doteq y + x
Indicating equality by definition in a vector space.
\vec{v} \doteq (x_1, x_2, \ldots, x_n)