Also observe that: * Disks whose ordinals have even parity move in the same sense as the smallest disk. Source: Internet
A triple is a surreal number system if and only if the following hold: * < is a total order over No * b is a function from No onto the class of all ordinals (b is called the "birthday function" on No). Source: Internet
Any limit of regular ordinals is a limit of initial ordinals and thus is also initial but need not be regular. Source: Internet
Chinese uses cardinal numbers in certain situations in which English would use ordinals. Source: Internet
Finally, he developed the multiplication operator, and proved that the surreals are actually a field, and that it includes both the reals and ordinals. Source: Internet
However, similar definitions can be made that eliminate the need for prior construction of the ordinals. Source: Internet