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
Empty map
Collection
Minimally disjoint collection of sets
N-wise disjoint set collection
Definition D1681
Disjoint set collection
Formulation 0
Let $X_j$ be a D11: Set for each $j \in J$.
Then $X = \{ X_j \}_{j \in J}$ is a disjoint set collection if and only if \begin{equation} \forall \, N \in 2, 3, 4, \ldots : \forall \, j_1, \ldots, j_N \in J \left( \forall \, n, m \in 1, \ldots, N \left( n \neq m \quad \implies \quad j_n \neq j_m \right) \quad \implies \quad \bigcap_{n = 1}^N X_{j_n} = \emptyset \right) \end{equation}