 It is also straightforward to show that the order type of the natural order on the ordinals restricted to the ordinals less than \(\alpha\) is \(\alpha\): the order on \(\{0, 1, 2\}\) is of order type 3, the order on the finite ordinals \(\{0, 1, 2, \ldots \}\) is the first infinite ordinal \(\omega\), and so forth.