\begin{definition}[Definition:Epsilon Relation]
In the language of set theory $\in$, the membership primitive, is neither a class nor a set, but a primitive predicate.
To simplify formulations, it is useful to introduce a class which behaves identically to the standard membership relation $\in$ for sets.
This class, denoted $\Epsilon$, will be referred to as the '''epsilon relation'''.
In class-builder notation:
:$\Epsilon := \set {\tuple {x, y}: x \in y}$
Thus, explicitly, $\Epsilon$ is a relation, taking arguments from ordered pairs of sets $x$ and $y$.
It consists of precisely those ordered pairs $\paren {x, y}$ satisfying $x \in y$.
The behaviour is thus seen to be identical to regular membership with sets.
It is '''not''' the same as class membership, because $x$ and $y$ must be set variables.
\end{definition}