A D18: Map $f : Y \to Z$ is an

**enclosed binary operation**on $X$ if and only if

(1) | $Y = X \times X$ |

(2) | $Z \subseteq X$ |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

Formulation 1

Let $X$ be a D11: Set.

A D554: Binary operation $f : X \times X \to Y$ on $X$ is**enclosed** if and only if
\begin{equation}
\forall \, x, y \in X : f(x, y) \in X
\end{equation}

A D554: Binary operation $f : X \times X \to Y$ on $X$ is

Formulation 2

Let $X$ be a D11: Set.

A D554: Binary operation $f : X \times X \to Y$ on $X$ is**enclosed** if and only if
\begin{equation}
Y \subseteq X
\end{equation}

A D554: Binary operation $f : X \times X \to Y$ on $X$ is

Also known as

Closed binary operation

Child definitions