\begin{definition}[Definition:Set/Distinction between Element and Set]
It is important to distinguish between an element, for example $a$, and a singleton containing it, that is, $\set a$.
That is $a$ and $\set a$ are ''not'' the same thing.
While it is true that:
:$a \in \set a$
it is not true that:
:$a = \set a$
neither is it true that:
:$a \in a$
\end{definition}