Definition:Set Union/General Definition

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Let $S$ be a collection, which could be either a set or a class.

The union of $S$ is:

$\ds \bigcup S := \set {x: \exists X \in S: x \in X}$

That is, the set of all elements of all elements of $S$ which are themselves sets.

Also denoted as

Some sources denote $\ds \bigcup S$ as $\ds \bigcup_{X \mathop \in S} X$.

Also see

  • Definition:Union of Set of Sets: subtly different from this, the assumption is that all elements of $S$ are in fact sets, whereas this more general version does not make that assumption.
  • Results about set union can be found here.
  • Results about class union can be found here.