Then transfinite induction tells us that formula 6 is true for all ordinals. Such ordinals are known as large countable ordinals. It is the supremum (least upper bound) of all countable ordinals. All of the ordinals discussed so far are still countable ordinals. Put more directly, it is the supremum of the set of smaller ordinals. Cantor called the set of finite ordinals the first number class. The class of all ordinals is a transitive class. Hence initial ordinals of cardinals remain initial in . Chinese uses cardinal numbers in certain situations in which English would use ordinals. A number system that includes the hyperreal numbers as well as the ordinals. Popes with unique names are not identified by ordinals. The result will be an infinite set of ordinals. The numbers 1 and 3 have irregular ordinals. Cantor normal form provides a standardized way of writing ordinals. The Cantor normal form provides a standardized way of writing ordinals.