there is a nonzero k < ! and a < such that = k + : Theorem 2 (Cantor Normal Form). Let be a nonzero ordinal. Then exist a nonzero natural number n, ordinals numb (*)

Oct 9, 2024 · Ordinal letters are the suffixes after the numeral (th, st). In general, treat ordinals the same as regular numbers: Spell out “first” through “ninth,” and use numerals for “10th” and above.

A Cardinal Number is a number that says how many of something there are, such as one, two, three, four, five. ... Note also that a Cardinal ending in "-y" becomes "-ieth" for the Ordinal.

Here, the idea is to (1) define an ordinal as a well-ordering which satisfies a relevant property, (2) use this property to construct a canonical sequence of ordinals, and (3) show that any well-ordering is …

We only care about the order of points in the ordinal, so two subsets ordered in the "same way" count as the same ordinal. For example, f0; 1; 2g and f 37; 3; g count as the same ordinal.

90 = ninety 100 = one hundred 101 = one hundred (and) one 1,000 = one thousand 1,001 = one thousand (and) one 1st = first 2nd = second 3rd = third 4th = fourth 5th = fifth 6th = sixth 7th = …

The endgoal of this section is to show that any ordinal has a canonical representative, which is something called an N-set (see below). Moreover, if we identify each ordinal with this canonical …