An *ordinal* is the order type of a well-ordered set.
Any two finite linear orderings of the same order type are isomorphic.

Finite orderings have order types which are natural numbers: `0,1,2,...`

.
The type of `(N,<)`

is `ω`

.
The type of the linear ordering which has all even natural numbers followed by all odd natural numbers is
`ω×2`

.

We avoid the *Burali-Forti paradox* by not letting the ordinals have an ordinal type.

Doets, Kees. *From Logic to Logic Programming.* MIT Press, 1994.

Copyright © 2014 Barry Watson. All rights reserved.