Subjects algebra

Groupoid Binary Operation

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Groupoid Binary Operation


1. The question asks whether a groupoid and a binary operation are the same and if they both come under algebraic structures. 2. A \textbf{binary operation} on a set $S$ is a function $*: S \times S \to S$, meaning it takes two elements from $S$ and returns another element in $S$. 3. A \textbf{groupoid} is a set $G$ together with a binary operation defined on it. So essentially, a groupoid is the pair $(G, *)$ where $*$ is a binary operation on $G$. 4. Therefore, a binary operation is not the same as a groupoid; the binary operation is part of the definition of a groupoid. 5. Both concepts are indeed part of the study of \textbf{algebraic structures}, which involves sets equipped with operations like binary operations. 6. Summary: A \textbf{binary operation} is a function while a \textbf{groupoid} is a set with a binary operation, so they are related but not the same.