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 |
| ▼ | Zermelo-Fraenkel set theory |
| ▼ | Set |
| ▼ | Binary cartesian set product |
| ▼ | Binary relation |
| ▼ | Map |
| ▼ | Operation |
| ▼ | N-operation |
| ▶ | D20: Enclosed binary operation |
| ▶ | D5319: 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 $x + y$.
|