Editing Well-order (section)

=== Natural numbers ===
The standard ordering ≤ of the [[natural number]]s is a well ordering and has the additional property that every non-zero natural number has a unique predecessor.

Another well ordering of the natural numbers is given by defining that all even numbers are less than all odd numbers, and the usual ordering applies within the evens and the odds:

:<math>\begin{matrix}
0 & 2 & 4 & 6 & 8 & \dots & 1 & 3 & 5 & 7 & 9 & \dots
\end{matrix}</math>

This is a well-ordered set of [[order type]] {{math|''ω'' + ''ω''}}. Every element has a successor (there is no largest element).  Two elements lack a predecessor: 0 and 1.