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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
Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...
The equation 2 ω = ω expresses the fact that finite sequences of zeros and ones can be identified with natural numbers, using the binary number system. The ordinal ω ω can be viewed as the order type of finite sequences of natural numbers; every element of ω ω (i.e. every ordinal smaller than ω ω) can be uniquely written in the form ...
The following table shows Odia ordinal numbers (Odia: ... Odia ordinal word Romanisation ୧: 1: ... 30: ତ୍ରିଂଶ ...
Numbers may either precede or follow their noun (see Latin word order). Most numbers are invariable and do not change their endings: regnāvit Ancus annōs quattuor et vīgintī (Livy) [1] 'Ancus reigned for 24 years' However, the numbers 1, 2, 3, and 200, 300, etc. change their endings for gender and grammatical case.
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:
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Cardinal and ordinal numbers must agree in gender (masculine or feminine; mixed groups are treated as masculine) with the noun they are describing. If there is no such noun (e.g. a telephone number or a house number in a street address), the feminine form is used. Ordinal numbers must also agree in number and definite status like other adjectives.