# Definition:Pairwise Disjoint/Family

< Definition:Pairwise Disjoint(Redirected from Definition:Pairwise Disjoint Family)

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## Definition

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**.

## Sources

- 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): $\S 1.2$: Operations on sets - 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 6$. Indexed families; partitions; equivalence relations