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Generalization of "n-th" to infinite cases
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite
Ordinal_number
Word representing the position or rank in a sequential order
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
Ordinal_numeral
Topics referred to by the same term
"third", and so on. Ordinal may also refer to: Ordinal number, an extension of ordinal numerals used to enumerate infinite sets Ordinal scale, ranking things
Ordinal
Character(s) following an ordinal number
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
Ordinal_indicator
Date written as number of days since first day of year
An ordinal date is a calendar date typically consisting of a year and an ordinal number, ranging between 1 and 366 (starting on January 1), representing
Ordinal_date
Mathematical technique used in proof theory
In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories
Ordinal_analysis
Regression analysis for modeling ordinal data
In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e.
Ordinal_regression
Statistical data type
Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are
Ordinal_data
theory, a branch of mathematics, an additively indecomposable ordinal α is any ordinal number that is not 0 such that for any β , γ < α {\displaystyle
Additively indecomposable ordinal
Additively_indecomposable_ordinal
Infinite ordinal number class
limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less
Limit_ordinal
Distinction between nominal, ordinal, interval and ratio variables
best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement
Level_of_measurement
Number used for counting
such as: "the third day of the month", in which case they are called ordinal numbers. Natural numbers are commonly expressed in writing using ten symbols
Natural_number
Operations on ordinals that extend classical arithmetic
In the mathematical field of set theory, ordinal arithmetic includes binary operations on ordinal numbers such as addition, multiplication, and exponentiation
Ordinal_arithmetic
Directions of north, south, east and west
(clockwise horizontal angle from north) are 0°, 90°, 180°, and 270°. The four ordinal directions or intercardinal directions are northeast (NE), southeast (SE)
Cardinal_direction
Set defined in terms of a finite number of ordinals by a first-order formula
said to be ordinal definable if, informally, it can be defined in terms of a finite number of ordinals by a first-order formula. Ordinal definable sets
Ordinal_definable_set
Names of numbers in English
zero at certain times of year. Ordinal numbers refer to a position (also called index or rank) in a sequence. Common ordinals include: Zeroth only has a meaning
English_numerals
In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers. They are useful in some transfinite
Even_and_odd_ordinals
Infinite cardinal number
infinite cardinal number ℵ α {\displaystyle \aleph _{\alpha }} for every ordinal number α , {\displaystyle \alpha ,} as described below. The concept and
Aleph_number
In set theory, an ordinal number α is an admissible ordinal if Lα is an admissible set (that is, a transitive model of Kripke–Platek set theory); in other
Admissible_ordinal
Preference ranking
In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that
Ordinal_utility
Smallest ordinal number that, considered as a set, is uncountable
uncountable ordinal, traditionally denoted by ω 1 {\displaystyle \omega _{1}} or sometimes by Ω {\displaystyle \Omega } , is the smallest ordinal number that
First_uncountable_ordinal
Ordinals in mathematics and set theory
countable ordinals. The smallest ones can be usefully and non-circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of relevance
Large_countable_ordinal
Topics referred to by the same term
mathematics, the Veblen ordinals is either of two Large countable ordinals: The Small Veblen ordinal The Large Veblen ordinal They are named after Oswald
Veblen_ordinal
Typographic abbreviation of the word "number(s)"
or no.), is a typographic abbreviation of the word number(s) indicating ordinal numeration, especially in names and titles. For example, using the numero
Numero_sign
Large countable ordinal
In mathematics, the Feferman–Schütte ordinal (Γ0) is a large countable ordinal. It is the proof-theoretic ordinal of several mathematical theories, such
Feferman–Schütte_ordinal
Order type of the set of all recursive ordinals
non-recursive ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using recursive ordinal notations
Nonrecursive_ordinal
2017 anime film by Tomohiko Itō
Sword Art Online the Movie: Ordinal Scale (Japanese: 劇場版 ソードアート・オンライン -オーディナル・スケール-, Hepburn: Gekijō-ban Sōdo Āto Onrain -Ōdinaru Sukēru-) is a 2017 Japanese
Sword Art Online the Movie: Ordinal Scale
Sword_Art_Online_the_Movie:_Ordinal_Scale
Operation on ordinal numbers
an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal. The ordinals 1
Successor_ordinal
International standards for dates and times
rules for determining the ordinal number of a calendar week in a year and a day within a week. ISO 2711: Representation of ordinal dates, issued in January
ISO_8601
Size of a possibly infinite set
order type; conversely, all finite ordinals have different cardinalities, and thus all finite ordinals are initial ordinals. Under their respective von Neumann
Cardinal_number
punctuation Korean punctuation Media control symbols Ordinal indicator – Character(s) following an ordinal number (used of the style 1st, 2nd, 3rd, 4th or
List of typographical symbols and punctuation marks
List_of_typographical_symbols_and_punctuation_marks
developmental psychology or non-human primate experiments, ordinal numerical competence or ordinal numerical knowledge is the ability to count objects in
Ordinal_numerical_competence
Two 16th-century Church of England liturgical books
The Edwardine Ordinals are two ordinals primarily written by Thomas Cranmer as influenced by Martin Bucer and first published under Edward VI, the first
Edwardine_Ordinals
Typographical symbol of a small circle
The number of the rank in question was indicated by ordinal numbers, in abbreviation with the ordinal indicator (a superscript letter ⟨o⟩). Use of "degree"
Degree_symbol
Set-theoretic function
an ordinal collapsing function (or projection function) is a technique for defining (notations for) certain recursive large countable ordinals, whose
Ordinal_collapsing_function
Large countable ordinal
Bachmann–Howard ordinal (also known as the Howard ordinal, or Howard–Bachmann ordinal) is a large countable ordinal. It is the proof-theoretic ordinal of several
Bachmann–Howard_ordinal
Number that is larger than all finite numbers
used to quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets. The term
Transfinite_number
Type of mathematical function
In mathematical logic and set theory, an ordinal notation is a partial function mapping the set of all finite sequences of symbols, themselves members
Ordinal_notation
Concept in heraldry
Regnal numbers are ordinal numbers—often written as Roman numerals—used to distinguish among persons with the same regnal name who held the same office
Regnal_number
Multiple-criteria decision analysis method
Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference
Ordinal_priority_approach
Relationship between items in a set
it is considered a tie. By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according
Ranking
Large countably-infinite ordinal number
mathematics, ψ0(Ωω), widely known as Buchholz's ordinal[citation needed], is a large countable ordinal that is used to measure the proof-theoretic strength
Buchholz's_ordinal
In mathematics, ordinal logic is a logic associated with an ordinal number by recursively adding elements to a sequence of previous logics. The concept
Ordinal_logic
Voting systems that use ranked ballots
preference among two or more candidates. Ranked voting systems that use ordinal numbers (1, 2, 3, etc.) such as IRV, STV and the Borda method are contrasted
Ranked_voting
Type of transfinite numbers
the von Neumann representation of ordinals. Larger ordinal fixed points of the exponential map are indexed by ordinal subscripts, resulting in ε 1 , ε
Epsilon_number
Certain large countable ordinal
the small Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. It is occasionally called the Ackermann ordinal, though the Ackermann
Small_Veblen_ordinal
Ordinal-indexed family of rapidly increasing functions
countable ordinal such that to every limit ordinal α < μ there is assigned a fundamental sequence (a strictly increasing sequence of ordinals whose supremum
Fast-growing_hierarchy
Natural number
collection of ten items (most often ten years) is called a decade. The ordinal form is tenth. The adjectives decimal and denary refer to systems or quantities
10
Set theory concept
smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the empty set is zero, and every ordinal has a rank
Von_Neumann_universe
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal one Ordinal 1st (first) Numeral system unary Factorization ∅ Divisors 1 Greek numeral
1
Certain topology in mathematics
finite ordinal, but no ordinal greater than ω is discrete. The ordinal α is compact as a topological space if and only if α is either a successor ordinal or
Order_topology
Liturgical book for ordinations
An ordinal (Latin: ordinale), in a modern context, is a liturgical book that contains the rites and prayers for the ordination and consecration to the
Ordinal_(liturgy)
Perceptual phenomenon
Ordinal-linguistic personification (OLP, or personification for short) is a form of synesthesia in which ordered sequences, such as ordinal numbers, days
Ordinal linguistic personification
Ordinal_linguistic_personification
Certain large countable ordinal
the large Veblen ordinal is a certain large countable ordinal, named after Oswald Veblen. There is no standard notation for ordinals beyond the Feferman–Schütte
Large_Veblen_ordinal
Study of mathematical algorithms for optimization problems
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria
Mathematical_optimization
Mathematical function on ordinals
functions from ordinals to ordinals), introduced by Oswald Veblen in Veblen (1908). If φ0 is any normal function, then for any non-zero ordinal α, φα is the
Veblen_function
Distance measure in statistics
a similarity measure that can handle different types of data (binary, ordinal, continuous) within the same dataset (unlike Hamming distance or Euclidean
Gower's_distance
Mathematical theorem
Since each well-ordered set is isomorphic to an ordinal, the theorem is also often stated in terms of ordinals. Transfinite recursion is an instance of transfinite
Transfinite_recursion_theorem
Generalization of the real numbers
as subfields of the surreals. The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations. It
Surreal_number
Countable ordinal that is the order type of a computable well-ordering of natural numbers
computable (or recursive) ordinal is an ordinal number that can be represented as a computable well-ordering of natural numbers. An ordinal α {\displaystyle
Computable_ordinal
1958 book by Wacław Sierpiński
Cardinal and Ordinal Numbers is a book on transfinite numbers, by Polish mathematician Wacław Sierpiński. It was published in 1958 by Państwowe Wydawnictwo
Cardinal_and_Ordinal_Numbers
Topological space in mathematics
using ordinal spaces that is a counterexample to several plausible-sounding conjectures. It is defined as the topological product of the two ordinal spaces
Tychonoff_plank
Isomorphism type of ordered sets
examples. Every well-ordered set is order-equivalent to exactly one ordinal number. The ordinal numbers are taken to be the canonical representatives of their
Order_type
Certain large countable ordinal
mathematics, the Ackermann ordinal is a certain large countable ordinal, named after Wilhelm Ackermann. The term "Ackermann ordinal" is also occasionally used
Ackermann_ordinal
Size of subsets in order theory
singular ordinal is any ordinal that is not regular. Every regular ordinal is the initial ordinal of a cardinal. Any limit of regular ordinals is a limit
Cofinality
Psychometric measurement scale
respects, to the extent to which Likert items are interpreted as being ordinal data.[citation needed] Two primary considerations guide the discussion
Likert_scale
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal seven Ordinal 7th (seventh) Numeral system septenary Factorization prime Prime 4th Divisors
7
Clade of insects
endo- "inner" + ptéryg- "wing" + Neo-Latin -ota "-having"), is a supra-ordinal clade of insects within the infraclass Neoptera that go through distinctive
Holometabola
Mathematician (1845–1918)
the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest
Georg_Cantor
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal two Ordinal 2nd (second) Numeral system binary Factorization prime Gaussian integer
2
Class of cardinal numbers
limit ordinal β is a weak limit cardinal. The ב operation can be used to obtain strong limit cardinals. This operation is a map from ordinals to cardinals
Limit_cardinal
Leap week calendar system
specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year. The Gregorian leap cycle, which has 97 leap days spread
ISO_week_date
Japanese light novel series and its adaptations
and December 2014. An animated film titled Sword Art Online the Movie: Ordinal Scale, featuring an original story by Kawahara, premiered in Japan and
Sword_Art_Online
Branch of mathematical logic
Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, proof-theoretic semantics, reverse mathematics
Proof_theory
Regression model for ordinal dependent variables
proportional odds logistic regression is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter
Ordered_logit
In computer programming, an ordinal data type is a data type with the property that its values can be counted. That is, the values can be put in a one-to-one
Ordinal_data_type
Galaxy containing the Solar System
Sun as the origin of the mapping system. Quadrants are described using ordinals – for example, "1st galactic quadrant", "second galactic quadrant", or
Milky_Way
Mathematical logic concept
It is a countable ordinal much smaller than large countable ordinals. To express ordinals in the language of arithmetic, an ordinal notation is needed
Gentzen's_consistency_proof
Large countable ordinal
theory and proof theory, the Takeuti–Feferman–Buchholz ordinal (TFBO) is a large countable ordinal, which acts as the limit of the range of Buchholz's psi
Takeuti–Feferman–Buchholz ordinal
Takeuti–Feferman–Buchholz_ordinal
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal five Ordinal 5th (fifth) Numeral system quinary Factorization prime Prime 3rd Divisors
5
Counting from "0" instead of "1" first
element, rather than the first element; zeroth is a coined word for the ordinal number zero. In some cases, an object or value that does not (originally)
Zero-based_numbering
An ordinal tree, by analogy with an ordinal number, is a rooted tree of arbitrary degree in which the children of each node are ordered, so that one refers
Ordinal_tree
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal four Ordinal 4th (fourth) Numeral system quaternary Factorization 22 Divisors 1, 2,
4
Statistic comparing ordinal rankings
of several statistics that measure an ordinal association — the relationship between rankings of different ordinal variables or different rankings of the
Rank_correlation
English poet and alchemist
English poet and alchemist best known for his 1477 alchemical poem, The Ordinal of Alchemy. This letter receiving, I hasted full sore To ride to my master
Thomas_Norton_(alchemist)
Punctuation to signal the end of a sentence (.)
the scalar product of two vectors. In many languages, an ordinal dot is used as the ordinal indicator. This applies mostly in Central and Northern Europe:
Full_stop
System of number names used in Georgian
This article contains Georgian text. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Georgian letters
Georgian_numerals
Type of infinite number in set theory
operations. An ordinal is a weakly inaccessible cardinal if and only if it is a regular ordinal and it is a limit of regular ordinals. (Zero, one, and
Inaccessible_cardinal
Type of cardinal number in mathematics
infinite ordinal α {\displaystyle \alpha } is a regular ordinal if it is a limit ordinal that is not the limit of a set of smaller ordinals that as a
Regular_cardinal
Paradox in set theory
the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a
Burali-Forti_paradox
Generalization of Turing computability
indexed by a countable ordinal number (ordinal), but not all countable ordinals correspond to a level of the hierarchy. The ordinals used by the hierarchy
Hyperarithmetical_theory
Natural number
List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal three Ordinal 3rd (third) Numeral system ternary Factorization prime Prime 2nd Divisors
3
Smallest cardinal strictly greater in size than another cardinal
similar way to the successor operation on the ordinal numbers. The cardinal successor coincides with the ordinal successor for finite cardinals, but in the
Successor_cardinal
Number used in combinatorial game theory
class as the ordinal numbers but endowed with nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication
Nimber
Mathematical concept
of mathematical induction to ordinal numbers. Its correctness is a theorem of ZF, and relies on the fact that the ordinal numbers are well-ordered, and
Transfinite_induction
Bit-vector representation where only one bit can be set at a time
either nominal or ordinal. Ordinal data has a ranked order for its values and can therefore be converted to numerical data through ordinal encoding. An example
One-hot
Topics referred to by the same term
Look up 1. in Wiktionary, the free dictionary. 1. is the ordinal form of the number one in a number of European languages. 1. may also refer to: 1. FC
1.
Last letter of the Greek alphabet
of functions. Chaitin's constant. In set theory, the first uncountable ordinal number, ω1 or Ω. The absolute infinite proposed by Georg Cantor. As part
Omega
Category of non-empty finite ordinals and order-preserving maps
(or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order-preserving maps. It is used to define
Simplex_category
Latin liturgical use in Britain
The Use of Sarum (or Use of Salisbury, also known as the Sarum Rite) is the liturgical use of the Latin rites developed at Salisbury Cathedral and used
Use_of_Sarum
ORDINAL
ORDINAL
ORDINAL
ORDINAL
Girl/Female
Hindu
To be reborn (Celebrity Name: Sushmita Sen)
Boy/Male
Arabic, Australian, Gujarati, Hindu, Indian, Kannada, Muslim, Pashtun, Sindhi
Judge; Honest; Just
Girl/Female
Biblical
Selling.
Boy/Male
Hindu
Ocean
Boy/Male
Hindu, Indian, Sanskrit
Boyhood
Girl/Female
American, Australian, British, English
Island of Linden Trees; From the Linden Tree Island; King's City Meadow
Boy/Male
Hindu, Indian, Tamil
To Bow in a Humble Greeting
Girl/Female
Hindu, Indian
Like a Flower
Male
English
English unisex name derived from the plant name briar, from Old English brer, BRIAR means "prickly bush."
Surname or Lastname
English
English : occupational name for a maker of wheels (for vehicles or for use in spinning or various other manufacturing processes), from an agent derivative of Middle English whele ‘wheel’. The name is particularly common on the Isle of Wight; on the mainland it is concentrated in the neighboring region of central southern England.A founder of Salisbury, NH, in 1634 was John Wheeler.
ORDINAL
ORDINAL
ORDINAL
ORDINAL
ORDINAL
a.
Next in order after the forty-ninth; -- the ordinal of fifty.
a.
Next in order after the twenty-ninth; the tenth after the twentieth; -- the ordinal of thirty; as, the thirtieth day of the month.
n.
Ordinal relation; position in the order of proceeding; as, he said in the first place.
a.
Indicating order or succession; as, the ordinal numbers, first, second, third, etc.
a.
Of or pertaining to an order.
n.
A word or number denoting order or succession.
a.
Next after the second; coming after two others; -- the ordinal of three; as, the third hour in the day.
a.
Next in order after the fourteenth; -- the ordinal of fifteen.
a.
Next in order after nine hundred and ninty-nine; coming last of a thousand successive individuals or units; -- the ordinal of thousand; as, the thousandth part of a thing.
a.
Next in order after the twelfth; the third after the tenth; -- the ordinal of thirteen; as, the thirteenth day of the month.
a.
Next in order after the fourth; -- the ordinal of five.
n.
The state or quality of being ordinal.
n.
The book of forms for making, ordaining, and consecrating bishops, priests, and deacons.
n.
A book containing the rubrics of the Mass.
a.
Next in order after the nineteenth; tenth after the tenth; coming after nineteen others; -- the ordinal of twenty.
n.
A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.
a.
Next in order after the eleventh; coming after eleven others; -- the ordinal of twelve.
a.
Next in order after the third; the ordinal of four.
a.
Preceding all others of a series or kind; the ordinal of one; earliest; as, the first day of a month; the first year of a reign.