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A recursive ordinal notation must satisfy the following two additional properties: the subset of natural numbers is a recursive set;
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 ...
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [ 1 ] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: These are smaller than any positive real number, but are nonetheless greater than zero.
This describes an ordinal notation: a system for naming ordinals over a finite alphabet. This particular system of ordinal notation is called the collection of arithmetical ordinal expressions, and can express all ordinals below ε 0, but cannot express ε 0.
Ordinal indicators are sometimes written as superscripts (1 st, 2 nd, 3 rd, 4 th, rather than 1st, 2nd, 3rd, 4th), although many English-language style guides recommend against this use. [4] Romance languages use a similar convention, such as 1 er or 2 e in French, or 4ª and 4º in Galician and Italian, or 4.ª and 4.º in Portuguese and Spanish.
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Ordinal numbers predate the invention of zero and positional notation. Ordinal numbers such as 21st, 33rd, etc., are formed by combining a cardinal ten with an ...