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
Relation
Definition D1048
N-ary relation
Formulation 1
Let $X_1, \ldots, X_N$ each be a D11: Set such that
(i) $\prod_{n = 1}^N X_n$ is a D326: Cartesian product for $X_1, \ldots, X_N$
An D548: Ordered pair $(X, R)$ is an N-ary relation on $\prod_{n = 1}^N X_n$ if and only if
(1) \begin{equation} X = \prod_{n = 1}^N X_n \end{equation}
(2) \begin{equation} R \subseteq \prod_{n = 1}^N X_n \end{equation}
Subdefinitions
D4: Binary relation