Definition:Set Union/Set of Sets

Definition
Let $\mathbb S$ be a set of sets.

The union of $\mathbb S$ is:
 * $\bigcup \mathbb S := \set {x: \exists X \in \mathbb S: x \in X}$

That is, the set of all elements of all elements of $\mathbb S$.

Thus the general union of two sets can be defined as:
 * $\bigcup \set {S, T} = S \cup T$

Also denoted as
The symbol $\bigcup$ is rendered in display mode as $\ds \bigcup$.

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

Also see

 * Axiom:Axiom of Unions (Set Theory)


 * Union of Doubleton for a proof that $\bigcup \set {S, T} = S \cup T$


 * Definition:Intersection of Set of Sets