Definition:Binary Operation/Also defined as

Binary Operation: Also defined as
Some authors specify that a binary operation $\circ$ is defined such that the codomain of $\circ$ is the same underlying set as that which forms the domain.

That is:
 * $\circ: S \times S \to S$

and thus gloss over the fact that a binary operation defined in such a way is closed.

Such a treatment can obscure the detail of the development of the theory of algebraic substructures; closedness is a fundamental concept in this context.