Definition:Pairwise Disjoint/Family

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An indexed family of sets $\family {S_i}_{i \mathop \in I}$ is said to be pairwise disjoint if and only if:

$\forall i, j \in I: i \ne j \implies S_i \cap S_j = \O$

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.