Meanings
plural ordinal numbers
- arithmeticA natural number used to denote position in a sequence.
In the expression a₃, the "3" is an ordinal number.
Synonyms: ordinal, ordinal numeral, ordinal, ordinal
- mathematicsSuch a number generalised to correspond to any cardinal number (the size of some set); formally, the order type of some well-ordered set of some cardinality a, which represents an equivalence class of well-ordered sets (exactly those of cardinality a) under the equivalence relation "existence of an order-preserving bijection".
3 more examples
1950, Frederick Bagemihl (translator), Erich Kamke, Theory of Sets, Dover (Dover Phoenix), 2006, page 137, For not only do the antinomies a) to e) disappear when we admit as elements of sets only such sets, ordinal numbers, and cardinal numbers as are bounded above by a fixed cardinal number, but we see also that paradoxes always arise if we collect into a set any sets, cardinal numbers, or ordinal numbers which are not bounded above by a fixed cardinal number.
1960 [D. Van Nostrand], Paul R. Halmos, Naive Set Theory, 2017, Dover, Republication, page 80, Is there a set that consists exactly of all the ordinal numbers? It is easy to see that the answer must be no. If there were such a set, then we could form the supremum of all ordinal numbers. That supremum would be an ordinal number greater than or equal to every ordinal number. Since, however, for each ordinal number there exists a strictly greater one (for example, its successor), this is impossible; it makes no sense to speak of the "set" of all ordinals.
If #92;alpha is an ordinal number, then by definition any two well-ordered sets of type #92;alpha are similar, i.e., there exists a one-to-one mapping from one set to the other. Consequently these sets have the same cardinality. Consequently to any ordinal number #92;alpha we may assign a cardinal number, the common cardinality of all well-ordered sets of type #92;alpha.
2009, Marek Kuczma, edited by Attila Gilányi, An Introduction to the Theory of Functional Equations and Inequalities, 2nd edition, Springer (Birkhäuser), page 10
Synonyms & antonyms
nounA natural number used to denote position in a sequence.
More synonyms by meaning
Synonym sets from Open English WordNet, CC BY 4.0.
Translations
Bulgarian числително редно, пореден номер
- числително редно (čislitelno redno)grammar: word used to denote relative position in a sequence
- пореден номер (poreden nomer)arithmetic: number used to denote position in a sequence
- ординалgeneralized kind of number to denote the length of a well-order on a set
Catalan nombre ordinal
- nombre ordinalgrammar: word used to denote relative position in a sequence
Chinese Mandarin 順序數 /顺序数, 序數 /序数
- 順序數 /顺序数 (shùnxùshù)grammar: word used to denote relative position in a sequence
- 序數 /序数 (xùshù)grammar: word used to denote relative position in a sequence
- 序數詞 /序数词 (xùshùcí)grammar: word used to denote relative position in a sequence
- 序數 /序数 (xùshù)arithmetic: number used to denote position in a sequence
Czech řadová číslovka, ordinální číslo
- řadová číslovkagrammar: word used to denote relative position in a sequence
- ordinální číslogeneralized kind of number to denote the length of a well-order on a set
Danish ordinaltal, ordenstal
- ordinaltalgrammar: word used to denote relative position in a sequence
- ordenstalgrammar: word used to denote relative position in a sequence
Dutch rangtelwoord, ranggetal
- rangtelwoordgrammar: word used to denote relative position in a sequence
- ranggetalgeneralized kind of number to denote the length of a well-order on a set
Finnish järjestyslukusana, ordinaalilukusana
- järjestyslukusanagrammar: word used to denote relative position in a sequence
- ordinaalilukusanagrammar: word used to denote relative position in a sequence
- järjestyslukuarithmetic: number used to denote position in a sequence
- ordinaalilukuarithmetic: number used to denote position in a sequence
- ordinaaligeneralized kind of number to denote the length of a well-order on a set
French nombre ordinal (pl. nombres ordinaux)
- nombre ordinal (pl. nombres ordinaux)grammar: word used to denote relative position in a sequence
German Ordnungszahl, Ordnungszahlwort
- Ordnungszahlgrammar: word used to denote relative position in a sequence
- Ordnungszahlwortgrammar: word used to denote relative position in a sequence
- Ordinalegrammar: word used to denote relative position in a sequence
- Ordinalzahlgrammar: word used to denote relative position in a sequence
Greek τακτικό αριθμητικό
- τακτικό αριθμητικό (taktikó arithmitikó)grammar: word used to denote relative position in a sequence
Hindi कर्मवाचक संख्या
- कर्मवाचक संख्या (karmvācak saṅkhyā)grammar: word used to denote relative position in a sequence
Hungarian sorszámnév, rendszám
- sorszámnévgrammar: word used to denote relative position in a sequence
- rendszámgeneralized kind of number to denote the length of a well-order on a set
Icelandic raðtala
- raðtalagrammar: word used to denote relative position in a sequence
Japanese 序数詞, 序数
- 序数詞 (josūshi)grammar: word used to denote relative position in a sequence
- 序数 (josū)grammar: word used to denote relative position in a sequence
- 順序数 (junjosū)generalized kind of number to denote the length of a well-order on a set
Korean 서수, 서수사
- 서수 (seosu)grammar: word used to denote relative position in a sequence
- 서수사 (seosusa)grammar: word used to denote relative position in a sequence
Latin numerus ordinālis
- numerus ordinālisgrammar: word used to denote relative position in a sequence
Māori tau raupapa
- tau raupapaarithmetic: number used to denote position in a sequence
Norwegian Bokmål ordenstall
- ordenstallgrammar: word used to denote relative position in a sequence
Polish liczebnik porządkowy, liczba porządkowa
- liczebnik porządkowygrammar: word used to denote relative position in a sequence
- liczba porządkowagrammar: word used to denote relative position in a sequence
- liczba porządkowaarithmetic: number used to denote position in a sequence
- liczba porządkowageneralized kind of number to denote the length of a well-order on a set
Portuguese número ordinal
- número ordinalgrammar: word used to denote relative position in a sequence
Russian поря́дковое числи́тельное, поря́дковый но́мер
- поря́дковое числи́тельное (porjádkovoje čislítelʹnoje)grammar: word used to denote relative position in a sequence
- поря́дковый но́мер (porjádkovyj nómer)arithmetic: number used to denote position in a sequence
- но́мер (nómer)arithmetic: number used to denote position in a sequence
Swedish ordningstal
- ordningstalgrammar: word used to denote relative position in a sequence
Tagalog bilang na panunod
- bilang na panunodarithmetic: number used to denote position in a sequence
Welsh trefnolyn, rhif trefnol
- trefnolyngrammar: word used to denote relative position in a sequence
- rhif trefnolgrammar: word used to denote relative position in a sequence
- trefnolynarithmetic: number used to denote position in a sequence
- rhif trefnolarithmetic: number used to denote position in a sequence
- trefnolyngeneralized kind of number to denote the length of a well-order on a set
- rhif trefnolgeneralized kind of number to denote the length of a well-order on a set
Cite this entry
ordinal number. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/ordinal%20number
“ordinal number.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/ordinal%20number. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “ordinal number,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/ordinal%20number.
Source: ordinal number on Wiktionary, CC BY-SA 4.0.