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.