Category:Definitions/Disjoint Unions

From ProofWiki
Jump to navigation Jump to search

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:

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