Definition:Ordering on Natural Numbers/Minimally Inductive Set

Definition
Let $\omega$ be the minimal infinite successor set.

The strict ordering of $\omega$ is the relation $<$ defined by:


 * $\forall m, n \in \omega: m < n \iff m \in n$

The (weak) ordering of $\omega$ is the relation $\le$ defined by:


 * $\forall m, n \in \omega: m \le n \iff m < n \lor m = n$