ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Definition D20
Enclosed binary operation
Formulation 0
Let $X$ be a D11: Set.
A D18: Map $f : Y \to Z$ is an enclosed binary operation on $X$ if and only if
(1) $Y = X \times X$
(2) $Z \subseteq X$
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}
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}
Children
Complex conjugation operation
Groupoid
Maximum operation
Minimum operation