Definition:Inductive Class

Definition
Let $A$ be a class.

Then $A$ is inductive :


 * $(1): \quad \O \in A$
 * $(2): \quad \forall x: \paren {x \in A \implies x^+ \in A}$

where $x^+$ is the successor of $x$.

That is, where:
 * $x^+ = x \cup \set x$

Inductive Set
The same definition can be applied when $A$ is a set: