Ordinal

An ordinal is called regular if it is cofinal with any smaller ordinal; otherwise it is singular.

Another "ordinal" date system ("ordinal" in the sense of advancing in value by one as the date advances by one day) is in common use in astronomical calculations and referencing and uses the same name as this "logistics" system.

Every regular ordinal is the initial ordinal of a cardinal.

If we use the von Neumann definition, under which each ordinal is identified as the set of all preceding ordinals, the paradox is unavoidable: the offending proposition that the order type of all ordinal numbers less than a fixed is itself must be true.

The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal.

The first ordinal number that is not a natural number is expressed as ω ; this is also the ordinal number of the set of natural numbers itself.

This is an ordinal number an individual assigns over the available actions, such as: : The individual's preferences are then expressed as the relation between these ordinal assignments.

To convert a Revised Julian date to any other calendar, first convert it to an ordinal day count, and then all that is needed is a function to convert the ordinal days count to that calendar.

Transfinite recursion Transfinite recursion is similar to transfinite induction; however, instead of proving that something holds for all ordinal numbers, we construct a sequence of objects, one for each ordinal.

As for the primary endpoint, changes in the World Health Organization’s 7-point ordinal scale, it has not trended any way so far.

He's also the main developer of the Ordinal Scale game.

No matter what game he plays, he becomes ridiculously capable almost immediately… with the exception of his appearance in Ordinal Scale, where he learned that real world fighting takes a little more than virtual battles do!

Rick Forzano, Belichick’s mentor who passed away, has an English Ordinal in sports gematria of 41. The letters “LA” equal 41 in sports gematria as well.

A cardinal is defined to be an equivalence class of similar classes (as opposed to ZFC, where a cardinal is a special sort of von Neumann ordinal).

Another criticism comes from the assertion that neither cardinal nor ordinal utility is empirically observable in the real world.

Approval Voting, Boston: Birkhäuser, p. 29 They also give a specific definition of a sincere approval vote in terms of the voter's ordinal preferences as being any vote that, if it votes for one candidate, it also votes for any more preferred candidate.

A relative record's key is its ordinal position; for example, the 10th record has a key of 10. This means that creating a record with a key of 5 may require the creation of (empty) preceding records.

Beside these documents, authorised liturgical formularies, such as Prayer Book and Ordinal, are normative.

British usage often changes the day from an integer to an ordinal, i.e., 21st instead of 21. In speech, "of" and "the" are used in the UK, as in "the 21st of April".

Cardinal, but not ordinal, addition commutes.