Search results
Results From The WOW.Com Content Network
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.
Pages in category "Ordinal numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...
In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing an explicit well-ordered set that represents the result of the operation or by using transfinite recursion .
The numero sign or numero symbol, № (also represented as Nº, No̱, №, No., or no.), [1] [2] is a typographic abbreviation of the word number(s) indicating ordinal numeration, especially in names and titles. For example, using the numero sign, the written long-form of the address "Number 29 Acacia Road" is shortened to "№ 29 Acacia Rd ...
Three well-orderings on the set of natural numbers with distinct order types (top to bottom): , +, and +. Every well-ordered set is order-equivalent to exactly one ordinal number , by definition. The ordinal numbers are taken to be the canonical representatives of their classes, and so the order type of a well-ordered set is usually identified ...
Since the epsilon numbers are an unbounded subclass of the ordinal numbers, they are enumerated using the ordinal numbers themselves. For any ordinal number , is the least epsilon number (fixed point of the exponential map) not already in the set {<}. It might appear that this is the non-constructive equivalent of the constructive definition ...
It contains ordinal notations for every computable ordinal, that is, ordinals below Church–Kleene ordinal, . Since ω 1 CK {\displaystyle \omega _{1}^{\text{CK}}} is the first ordinal not representable in a computable system of ordinal notations the elements of O {\displaystyle {\mathcal {O}}} can be regarded as the canonical ordinal notations.
Ordinal indicator, the sign adjacent to a numeral denoting that it is an ordinal number; Ordinal number in set theory, a number type with order structures; Ordinal number (linguistics), a word representing the rank of a number; Ordinal scale, ranking things that are not necessarily numbers; Ordinal utility (economics): a utility function which ...