# Definition:Pairwise Disjoint/Set of Sets

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

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## Definition

A set of sets $\Bbb S$ is said to be **pairwise disjoint** if and only if:

- $\forall X, Y \in \Bbb S: X \ne Y \implies X \cap Y = \O$

Here, $\cap$ denotes intersection, and $\O$ denotes the empty set.

Hence we can say that the elements of $\Bbb S$ are **pairwise disjoint**.

## Also known as

Such a set of sets, whose elements are **pairwise disjoint**, is often referred to as a **pairwise disjoint collection**.

Other names for **pairwise disjoint** include **mutually disjoint** and **non-intersecting**.

## Sources

- 1960: Paul R. Halmos:
*Naive Set Theory*... (previous) ... (next): $\S 4$: Unions and Intersections - 1966: Richard A. Dean:
*Elements of Abstract Algebra*... (previous) ... (next): $\S 0.2$ - 1967: George McCarty:
*Topology: An Introduction with Application to Topological Groups*... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Relations - 1971: Robert H. Kasriel:
*Undergraduate Topology*... (previous) ... (next): $\S 1.20$: Decomposition of a Set: Definition $20.1$