Natural Numbers are Comparable

Theorem
Let $\N$ be the natural numbers, defined as the minimal infinite successor set $\omega$.

Let $m, n \in \N$.

Then exactly one of the following is the case:
 * $(1): \quad m \in n$
 * $(2): \quad m = n$
 * $(3): \quad n \in m$

That is, two natural numbers are always comparable by the ordering $\le$ where:
 * $m \le n \iff \begin{cases}

m = n & \text{or}\\ m \in n & \end{cases}$