\begin{definition}[Definition:Set Union/Set of Sets]
Let $\mathbb S$ be a set of sets.
The '''union of $\mathbb S$''' is:
:$\ds \bigcup \mathbb S := \set {x: \exists X \in \mathbb S: x \in X}$
That is, the set of all elements of all elements of $\mathbb S$.
Thus the general union of two sets can be defined as:
:$\ds \bigcup \set {S, T} = S \cup T$
\end{definition}