Binary operation

A binary operation ∘ is a rule for combining the arguments a and b (called operands) to produce a ∘ b $$ a ∘ b \rightarrow c $$ It's an operation of arity two.

A binary operation ∘ on a set S is an internal operation (closed operation) because a,b,c are elements of the same set

$$ a ∘ b \rightarrow c \ \ \ \ a,b,c \in S $$

Domain and the codomain are the same set.

$$ ∘: S \rightarrow S $$