# Definition:Inductive Class

## Definition

Let $A$ be a class.

Then $A$ is inductive if and only if:

$(1): \quad \varnothing \in A$
$(2): \quad \forall x: \left({x \in A \implies x^+ \in A}\right)$

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

That is, where:

$x^+ = x \cup \left\{{x}\right\}$