Definition:Set/Distinction between Element and Set

Definition
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:
 * $a \in a$