\begin{definition}[Definition:Set Equality/Definition 1]
Let $S$ and $T$ be sets.
$S$ and $T$ are equal {{iff}} they have the same elements:
:$S = T \iff \paren {\forall x: x \in S \iff x \in T}$
Otherwise, $S$ and $T$ are '''distinct''', or '''unequal'''.
\end{definition}