# Definition:Domain (Set Theory)/Binary Operation

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## Definition

Let $\circ: S \times S \to T$ be a binary operation.

The **domain** of $\circ$ is the set $S$ and can be denoted $\operatorname{Dom} \left({\circ}\right)$.

This definition can be considered as the same as that for the **domain** of a mapping, where the domain would be defined as $S \times S$.