User:Dfeuer/Definition:Inductive Class

Definition

Let $A$ be a class.

Then $A$ is inductive iff:

$(1) \quad \varnothing \in A$

$(2) \quad \forall x: (x \in A \implies x^+ \in A)$

where $x^+$ is the Definition:Successor Set of $x$: $x^+ = x \cup \{x\}$