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Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced. For example: 5 November 1605 (pronounced "the fifth of November ...
The same suffix may be used with more than one category of number, as for example the orginary numbers secondary and tertiary and the distributive numbers binary and ternary. For the hundreds, there are competing forms: Those in -gent-, from the original Latin, and those in -cent-, derived from centi-, etc. plus the prefixes for 1 through 9 .
When indicating dates, suffixes are never used. Examples: 1:a klass "first grade (in elementary school)", 3:e utgåvan "third edition", but 6 november. Furthermore, suffixes can be left out if the number obviously is an ordinal number, example: 3 utg. "3rd ed".
Cantor's work with derived sets and ordinal numbers led to the Cantor-Bendixson theorem. [14] Using successors, limits, and cardinality, Cantor generated an unbounded sequence of ordinal numbers and number classes. [15] The (α + 1)-th number class is the set of ordinals whose predecessors form a set of the same cardinality as the α-th
The suffixes -th, -st, -nd and -rd are occasionally written superscript above the number itself. If the tens digit of a number is 1, then "th" is written after the number. For example: 13th, 19th, 112th, 9,311th. If the tens digit is not equal to 1, then the following table could be used:
The von Neumann cardinal assignment is a cardinal assignment that uses ordinal numbers. For a well-orderable set U, we define its cardinal number to be the smallest ordinal number equinumerous to U, using the von Neumann definition of an ordinal number. More precisely:
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. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω.
Use {{ordinal | integer | sup = yes}} to display the ordinal suffix in superscript. Do not use superscript notation in the article space, per this section of the Manual of Style. For integers ending in 1, 2 or 3 (except for integers ending in 11, 12 or 13), the ordinal suffixes will be -st, -nd and -rd, respectively.
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