# Category:Definitions/Disjoint Unions

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This category contains definitions related to Disjoint Union in the context of Set Theory.

Related results can be found in Category:Disjoint Unions.

Let $\family {S_i}_{i \mathop \in I}$ be an $I$-indexed family of sets.

The **disjoint union** of $\family {S_i}_{i \mathop \in I}$ is defined as the set:

- $\ds \bigsqcup_{i \mathop \in I} S_i = \bigcup_{i \mathop \in I} \set {\tuple {x, i}: x \in S_i}$

where $\bigcup$ denotes union.

Each of the sets $S_i$ is canonically embedded in the **disjoint union** as the set:

- ${S_i}^* = \set {\tuple {x, i}: x \in S_i}$

## Pages in category "Definitions/Disjoint Unions"

The following 5 pages are in this category, out of 5 total.