\begin{definition}[Definition:Set Union/General Definition]
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.
\end{definition}