Order Type of Integers under Usual Ordering

Theorem
Consider the ordered structure $\struct {\Z, \le}$ that is the set of integers under the usual ordering.

Then:
 * $\map \ot {\Z, \le} = \omega^* + \omega$

where:
 * $\ot$ denotes order type
 * $\omega$ denotes the order type of the natural numbers $\N$
 * $\omega^*$ denotes the dual of $\omega$
 * $+$ denotes addition of order types.