Ordinal number
Elementary
An ordinal number is a number that tells position of an item in a list, such the first, second, and third runner in a race.
High school
An ordinal number is a number that tells position of an item in a list, such the first, second, and third.
Graduate (set theory)
An ordinal number is the order type of a well-ordered set. The finite ordinals are the natural numbers, followed by infinite ordinals $\omega, \omega + 1, \omega + 2, \dots$
Examples
Non-examples
Things that may be mistaken for examples.
- A phone number Elementary
Properties
- For infinite sets, ordinals and cardinals differ: $\omega$ and $\omega + 1$ are different ordinals, but the corresponding sets have the same cardinality, $\aleph_0$.