Jump to navigation Jump to search
- $\forall i, j \in I: i \ne j \implies S_i \cap S_j = \O$
Hence the indexed sets $S_i$ themselves, where $i \in I$, are referred to as being pairwise disjoint.
Also known as
Other names for pairwise disjoint include mutually disjoint and non-intersecting.
Some sources use the compact term disjoint family.
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Subsets and Complements; Union and Intersection
- 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $1$ Set Theory: $1$. Sets and Functions: $1.2$: Operations on sets
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 6$. Indexed families; partitions; equivalence relations