\begin{definition}[Definition:Set Union]
Let $S$ and $T$ be sets.
The '''(set) union''' of $S$ and $T$ is the set $S \cup T$, which consists of all the elements which are contained in either (or both) of $S$ and $T$:
:$x \in S \cup T \iff x \in S \lor x \in T$
or, slightly more formally:
:$A = S \cup T \iff \forall z: \paren {z \in A \iff z \in S \lor z \in T}$
We can write:
:$S \cup T := \set {x: x \in S \lor x \in T}$
and can voice it '''$S$ union $T$'''.
It can be seen that, in this form, $\cup$ is a binary operation which acts on sets.
\end{definition}