Let $X$ be a D11: Set.
A D18: Map $f : Y \to Z$ is a binary operation on $X$ if and only if
\begin{equation}
Y = X \times X
\end{equation}
▼  Set of symbols 
▼  Alphabet 
▼  Deduction system 
▼  Theory 
▼  ZermeloFraenkel set theory 
▼  Set 
▼  Binary cartesian set product 
▼  Binary relation 
▼  Map 
▼  Operation 
▼  Noperation 
▶  Enclosed binary operation 
▶  Idempotent binary operation 
▶ 
Convention 0
(Multiplicative notation)
Let $X \neq \emptyset$ be a D11: Set and let $f : X \times X \to Y$ be a D554: Binary operation on $X$. If $x, y \in X$, then the convention in multiplicative notation is to denote the element $f(x, y)$ by $x y$.

▶ 
Convention 1
(Additive notation)
Let $X \neq \emptyset$ be a D11: Set and let $f : X \times X \to Y$ be a D554: Binary operation on $X$. If $x, y \in X$, then the convention in additive notation is to denote the element $f(x, y)$ by $x + y$.
