Def/Empty set

 =Construction= Consider the unary predicate $E(x)$, given by "$x \neq x$". The corresponding class, $\{ x \vert x \neq x \}$ is "empty", in the sense that no set is in this class.

The axiom of selection, together with the existence of a set implies that the class $\{ x \vert x \neq x \}$ is representable by a set. The resulting set is called $\emptyset$. To guarantee the existence of a set, it is perhaps most convenient to assume the existence of the empty set, with the relies on::State/Axiom of the empty set.

=Uniqueness= The uniqueness of the empty set follows from the axiom of extensionality.

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