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Cardinal versus ordinal numbers. In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance, chronology, and so on (e.g., "third", "tertiary"). They differ from cardinal numerals, which represent quantity (e.g., "three") and other types of numerals.
Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: simplex, duplex (communication in only 1 direction at a time, in 2 directions simultaneously) unicycle, bicycle, tricycle (vehicle with 1 wheel, 2 wheels ...
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.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
In written languages, an ordinal indicator is a character, or group of characters, following a numeral denoting that it is an ordinal number, rather than a cardinal number. In English orthography , this corresponds to the suffixes ‑st , ‑nd , ‑rd , ‑th in written ordinals (represented either on the line 1st , 2nd , 3rd , 4th or as ...
An ordinal number may also be used to describe the notion of "size" for a well-ordered set, in a sense different from cardinality: if there is an order isomorphism (more than a bijection) between two well-ordered sets, they have the same ordinal number. The first ordinal number that is not a natural number is expressed as ω; this is also the ...
Main article: list of numeral systems. Decimal: The standard Hindu–Arabic numeral system using base ten. Binary: The base-two numeral system used by computers, with digits 0 and 1. Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits.
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: where ON is the class of ordinals. This ordinal is also called the initial ...