Binary operation

A binary operation, denoted as ∘, is a procedure that combines two arguments, a and b (referred to as operands), to yield a result: $$ a ∘ b \rightarrow c $$ This operation has an arity of two.

When a binary operation ∘ is defined on a set S, it is termed an internal or closed operation. This is because the operands a, b, and the result c all belong to the same set S:

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

Both the domain and the codomain of this operation are the set S:

$$ ∘: S \rightarrow S $$