\begin{definition}[Definition:Ordering on Natural Numbers/Minimal Infinite Successor Set]
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:
:$\forall m, n \in \omega: m \le n \iff m < n \lor m = n$
Category:Definitions/Minimal Infinite Successor Set
Category:Definitions/Ordering on Natural Numbers
\end{definition}