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.
$$ ∘: S \rightarrow S $$