Definition:Ordering on Natural Numbers/Von Neumann Construction

Definition
Let $\omega$ denote the set of natural numbers as defined by the von Neumann construction.

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


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

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


 * $\forall m, n \in \omega: m \le n \iff m \subseteq n$