See ordinal number in All languages combined, or Wiktionary
{ "antonyms": [ { "english": "grammar", "tags": [ "cardinal", "numeral" ], "word": "antonym(s) of" } ], "coordinate_terms": [ { "_dis1": "7 50 43", "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "cardinal number" }, { "_dis1": "7 50 43", "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "distributive number" }, { "_dis1": "7 50 43", "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "multiplier" } ], "forms": [ { "form": "ordinal numbers", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "ordinal number (plural ordinal numbers)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "_dis1": "7 50 43", "word": "numeral" }, { "_dis1": "7 50 43", "word": "order type" }, { "_dis1": "7 50 43", "word": "zeroth" } ], "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Grammar", "orig": "en:Grammar", "parents": [ "Linguistics", "Language", "Social sciences", "Communication", "Sciences", "Society", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "text": "First, second and third are the ordinal numbers corresponding to one, two and three.", "type": "example" } ], "glosses": [ "A word that expresses the relative position of an item in a sequence." ], "id": "en-ordinal_number-en-noun-P3hkQnMQ", "links": [ [ "grammar", "grammar" ], [ "relative", "relative" ], [ "position", "position" ], [ "sequence", "sequence" ] ], "raw_glosses": [ "(grammar) A word that expresses the relative position of an item in a sequence." ], "topics": [ "grammar", "human-sciences", "linguistics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Arithmetic", "orig": "en:Arithmetic", "parents": [ "Applied sciences", "Mathematics", "Sciences", "Formal sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "5 56 40", "kind": "topical", "langcode": "en", "name": "Numbers", "orig": "en:Numbers", "parents": [ "All topics", "Terms by semantic function", "Fundamental" ], "source": "w+disamb" } ], "examples": [ { "text": "In the expression a₃, the \"3\" is an ordinal number.", "type": "example" } ], "glosses": [ "A natural number used to denote position in a sequence." ], "id": "en-ordinal_number-en-noun-IL2J4R9M", "links": [ [ "arithmetic", "arithmetic" ], [ "natural number", "natural number" ], [ "position", "position" ], [ "sequence", "sequence" ] ], "raw_glosses": [ "(arithmetic) A natural number used to denote position in a sequence." ], "topics": [ "arithmetic" ], "translations": [ { "_dis1": "23 67 10", "code": "ca", "lang": "Catalan", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "nombre ordinal" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "順序數" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "roman": "shùnxùshù", "sense": "grammar: word used to denote relative position in a sequence", "word": "顺序数" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "序數" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshù", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "序數詞" }, { "_dis1": "23 67 10", "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshùcí", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数词" }, { "_dis1": "23 67 10", "code": "crh", "lang": "Crimean Tatar", "sense": "grammar: word used to denote relative position in a sequence", "word": "sıra sayısı" }, { "_dis1": "23 67 10", "code": "cs", "lang": "Czech", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "řadová číslovka" }, { "_dis1": "23 67 10", "code": "da", "lang": "Danish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordinaltal" }, { "_dis1": "23 67 10", "code": "da", "lang": "Danish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordenstal" }, { "_dis1": "23 67 10", "code": "nl", "lang": "Dutch", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "rangtelwoord" }, { "_dis1": "23 67 10", "code": "fo", "lang": "Faroese", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "raðtal" }, { "_dis1": "23 67 10", "code": "fi", "lang": "Finnish", "sense": "grammar: word used to denote relative position in a sequence", "word": "järjestyslukusana" }, { "_dis1": "23 67 10", "code": "fi", "lang": "Finnish", "sense": "grammar: word used to denote relative position in a sequence", "word": "ordinaalilukusana" }, { "_dis1": "23 67 10", "code": "fr", "lang": "French", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "nombre ordinal (pl. nombres ordinaux)" }, { "_dis1": "23 67 10", "code": "gl", "lang": "Galician", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "número ordinal" }, { "_dis1": "23 67 10", "code": "ka", "lang": "Georgian", "roman": "rigobiti ricxviti saxeli", "sense": "grammar: word used to denote relative position in a sequence", "word": "რიგობითი რიცხვითი სახელი" }, { "_dis1": "23 67 10", "code": "ka", "lang": "Georgian", "roman": "rigiti ricxviti saxeli", "sense": "grammar: word used to denote relative position in a sequence", "word": "რიგითი რიცხვითი სახელი" }, { "_dis1": "23 67 10", "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "Ordnungszahl" }, { "_dis1": "23 67 10", "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "Ordnungszahlwort" }, { "_dis1": "23 67 10", "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "Ordinale" }, { "_dis1": "23 67 10", "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "Ordinalzahl" }, { "_dis1": "23 67 10", "code": "el", "lang": "Greek", "roman": "taktikó arithmitikó", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "τακτικό αριθμητικό" }, { "_dis1": "23 67 10", "code": "hi", "lang": "Hindi", "roman": "karmvācak saṅkhyā", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "कर्मवाचक संख्या" }, { "_dis1": "23 67 10", "code": "hu", "lang": "Hungarian", "sense": "grammar: word used to denote relative position in a sequence", "word": "sorszámnév" }, { "_dis1": "23 67 10", "code": "is", "lang": "Icelandic", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "raðtala" }, { "_dis1": "23 67 10", "alt": "じょすうし", "code": "ja", "lang": "Japanese", "roman": "josūshi", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数詞" }, { "_dis1": "23 67 10", "alt": "じょすう", "code": "ja", "lang": "Japanese", "roman": "josū", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数" }, { "_dis1": "23 67 10", "code": "ko", "lang": "Korean", "roman": "seosu", "sense": "grammar: word used to denote relative position in a sequence", "word": "서수" }, { "_dis1": "23 67 10", "code": "ko", "lang": "Korean", "roman": "seosusa", "sense": "grammar: word used to denote relative position in a sequence", "word": "서수사" }, { "_dis1": "23 67 10", "code": "nb", "lang": "Norwegian Bokmål", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordenstall" }, { "_dis1": "23 67 10", "code": "pl", "lang": "Polish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "inanimate", "masculine" ], "word": "liczebnik porządkowy" }, { "_dis1": "23 67 10", "code": "pl", "lang": "Polish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "_dis1": "23 67 10", "code": "pt", "lang": "Portuguese", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "número ordinal" }, { "_dis1": "23 67 10", "code": "ru", "lang": "Russian", "roman": "porjádkovoje čislítelʹnoje", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "поря́дковое числи́тельное" }, { "_dis1": "23 67 10", "code": "sh", "lang": "Serbo-Croatian", "sense": "grammar: word used to denote relative position in a sequence", "word": "redni broj" }, { "_dis1": "23 67 10", "code": "sv", "lang": "Swedish", "sense": "grammar: word used to denote relative position in a sequence", "word": "ordningstal" }, { "_dis1": "23 67 10", "code": "cy", "lang": "Welsh", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "trefnolyn" }, { "_dis1": "23 67 10", "code": "cy", "lang": "Welsh", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "rhif trefnol" }, { "_dis1": "9 84 7", "code": "cmn", "lang": "Chinese Mandarin", "sense": "arithmetic: number used to denote position in a sequence", "word": "序數" }, { "_dis1": "9 84 7", "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshù", "sense": "arithmetic: number used to denote position in a sequence", "word": "序数" }, { "_dis1": "9 84 7", "code": "fi", "lang": "Finnish", "sense": "arithmetic: number used to denote position in a sequence", "word": "järjestysluku" }, { "_dis1": "9 84 7", "code": "fi", "lang": "Finnish", "sense": "arithmetic: number used to denote position in a sequence", "word": "ordinaaliluku" }, { "_dis1": "9 84 7", "code": "mi", "lang": "Maori", "sense": "arithmetic: number used to denote position in a sequence", "word": "tau raupapa" }, { "_dis1": "9 84 7", "code": "pl", "lang": "Polish", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "_dis1": "9 84 7", "code": "ru", "lang": "Russian", "roman": "porjádkovyj nómer", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "поря́дковый но́мер" }, { "_dis1": "9 84 7", "code": "ru", "lang": "Russian", "roman": "nómer", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "но́мер" }, { "_dis1": "9 84 7", "code": "tl", "lang": "Tagalog", "sense": "arithmetic: number used to denote position in a sequence", "word": "bilang na panunod" }, { "_dis1": "9 84 7", "code": "cy", "lang": "Welsh", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "trefnolyn" }, { "_dis1": "9 84 7", "code": "cy", "lang": "Welsh", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "rhif trefnol" }, { "_dis1": "5 54 41", "code": "cs", "lang": "Czech", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "neuter" ], "word": "ordinální číslo" }, { "_dis1": "5 54 41", "code": "nl", "lang": "Dutch", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "neuter" ], "word": "ranggetal" }, { "_dis1": "5 54 41", "code": "fi", "lang": "Finnish", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "ordinaali" }, { "_dis1": "5 54 41", "code": "hu", "lang": "Hungarian", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "rendszám" }, { "_dis1": "5 54 41", "alt": "じゅんじょすう", "code": "ja", "lang": "Japanese", "roman": "junjosū", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "順序数" }, { "_dis1": "5 54 41", "code": "pl", "lang": "Polish", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "_dis1": "5 54 41", "code": "cy", "lang": "Welsh", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "masculine" ], "word": "trefnolyn" }, { "_dis1": "5 54 41", "code": "cy", "lang": "Welsh", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "masculine" ], "word": "rhif trefnol" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Set theory", "orig": "en:Set theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "18 18 64", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "8 15 76", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "12 20 67", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "8 13 79", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "15 24 62", "kind": "other", "name": "Terms with Afrikaans translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 63", "kind": "other", "name": "Terms 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"parents": [], "source": "w+disamb" }, { "_dis": "14 27 59", "kind": "other", "name": "Terms with Georgian translations", "parents": [], "source": "w+disamb" }, { "_dis": "10 24 66", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "18 30 51", "kind": "other", "name": "Terms with Greek translations", "parents": [], "source": "w+disamb" }, { "_dis": "21 21 58", "kind": "other", "name": "Terms with Hindi translations", "parents": [], "source": "w+disamb" }, { "_dis": "18 27 55", "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "12 22 66", "kind": "other", "name": "Terms with Icelandic translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 62", "kind": "other", "name": "Terms with Irish translations", "parents": [], "source": "w+disamb" }, { "_dis": "11 21 68", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "10 19 71", "kind": "other", "name": "Terms with Japanese translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 63", "kind": "other", "name": "Terms with Korean translations", "parents": [], "source": "w+disamb" }, { "_dis": "17 28 55", "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 63", "kind": "other", "name": "Terms with Maori translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 26 60", "kind": "other", "name": "Terms with Norwegian Bokmål translations", "parents": [], "source": "w+disamb" }, { "_dis": "9 12 79", "kind": "other", "name": "Terms with Norwegian Nynorsk translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 26 61", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 27 58", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 63", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "11 21 68", "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 22 65", "kind": "other", "name": "Terms with Serbo-Croatian translations", "parents": [], "source": "w+disamb" }, { "_dis": "10 20 70", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "12 21 67", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" }, { "_dis": "13 24 62", "kind": "other", "name": "Terms with Tagalog translations", "parents": [], "source": "w+disamb" }, { "_dis": "15 24 62", "kind": "other", "name": "Terms with Vietnamese translations", "parents": [], "source": "w+disamb" }, { "_dis": "12 26 62", "kind": "other", "name": "Terms with Welsh translations", "parents": [], "source": "w+disamb" }, { "_dis": "11 16 74", "kind": "other", "langcode": "en", "name": "Parts of speech", "orig": "en:Parts of speech", "parents": [], "source": "w+disamb" } ], "examples": [ { "text": "1950, Frederick Bagemihl (translator), Erich Kamke, Theory of Sets, Dover (Dover Phoenix), 2006, page 137,\nFor 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." }, { "text": "1960 [D. Van Nostrand], Paul R. Halmos, Naive Set Theory, 2017, Dover, Republication, page 80,\nIs 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." }, { "text": "2009, Marek Kuczma, Attila Gilányi (editor), An Introduction to the Theory of Functional Equations and Inequalities, Springer (Birkhäuser), 2nd Edition, page 10,\nIf α is an ordinal number, then by definition any two well-ordered sets of type α 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 α we may assign a cardinal number, the common cardinality of all well-ordered sets of type α." } ], "glosses": [ "Such 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\"." ], "id": "en-ordinal_number-en-noun-1aenKer8", "links": [ [ "set theory", "set theory" ], [ "cardinal number", "cardinal number" ], [ "set", "set" ], [ "order type", "order type" ], [ "well-ordered", "well-ordered" ], [ "cardinality", "cardinality" ], [ "equivalence class", "equivalence class" ], [ "equivalence relation", "equivalence relation" ], [ "bijection", "bijection" ] ], "raw_glosses": [ "(set theory) Such 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\"." ], "topics": [ "mathematics", "sciences", "set-theory" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Vealhurl-ordinal number.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav.ogg" } ], "synonyms": [ { "_dis1": "7 50 43", "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "ordinal" }, { "_dis1": "7 50 43", "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "ordinal numeral" }, { "_dis1": "7 50 43", "topics": [ "arithmetic" ], "word": "ordinal" }, { "_dis1": "7 50 43", "topics": [ "order-theory", "mathematics", "sciences" ], "word": "ordinal" } ], "wikipedia": [ "ordinal number" ], "word": "ordinal number" }
{ "antonyms": [ { "english": "grammar", "tags": [ "cardinal", "numeral" ], "word": "antonym(s) of" } ], "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Requests for review of Afrikaans translations", "Requests for review of Dutch translations", "Requests for review of French translations", "Requests for review of Icelandic translations", "Requests for review of Irish translations", "Requests for review of Italian translations", "Requests for review of Norwegian Nynorsk translations", "Requests for review of Romanian translations", "Requests for review of Spanish translations", "Requests for review of Swedish translations", "Requests for review of Vietnamese translations", "Terms with Afrikaans translations", "Terms with Catalan translations", "Terms with Crimean Tatar translations", "Terms with Czech translations", "Terms with Danish translations", "Terms with Dutch translations", "Terms with Faroese translations", "Terms with Finnish translations", "Terms with French translations", "Terms with Galician translations", "Terms with Georgian translations", "Terms with German translations", "Terms with Greek translations", "Terms with Hindi translations", "Terms with Hungarian translations", "Terms with Icelandic translations", "Terms with Irish translations", "Terms with Italian translations", "Terms with Japanese translations", "Terms with Korean translations", "Terms with Mandarin translations", "Terms with Maori translations", "Terms with Norwegian Bokmål translations", "Terms with Norwegian Nynorsk translations", "Terms with Polish translations", "Terms with Portuguese translations", "Terms with Romanian translations", "Terms with Russian translations", "Terms with Serbo-Croatian translations", "Terms with Spanish translations", "Terms with Swedish translations", "Terms with Tagalog translations", "Terms with Vietnamese translations", "Terms with Welsh translations", "en:Numbers", "en:Parts of speech" ], "coordinate_terms": [ { "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "cardinal number" }, { "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "distributive number" }, { "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "multiplier" } ], "forms": [ { "form": "ordinal numbers", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "ordinal number (plural ordinal numbers)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "related": [ { "word": "numeral" }, { "word": "order type" }, { "word": "zeroth" } ], "senses": [ { "categories": [ "English terms with usage examples", "en:Grammar" ], "examples": [ { "text": "First, second and third are the ordinal numbers corresponding to one, two and three.", "type": "example" } ], "glosses": [ "A word that expresses the relative position of an item in a sequence." ], "links": [ [ "grammar", "grammar" ], [ "relative", "relative" ], [ "position", "position" ], [ "sequence", "sequence" ] ], "raw_glosses": [ "(grammar) A word that expresses the relative position of an item in a sequence." ], "topics": [ "grammar", "human-sciences", "linguistics", "sciences" ] }, { "categories": [ "English terms with usage examples", "en:Arithmetic" ], "examples": [ { "text": "In the expression a₃, the \"3\" is an ordinal number.", "type": "example" } ], "glosses": [ "A natural number used to denote position in a sequence." ], "links": [ [ "arithmetic", "arithmetic" ], [ "natural number", "natural number" ], [ "position", "position" ], [ "sequence", "sequence" ] ], "raw_glosses": [ "(arithmetic) A natural number used to denote position in a sequence." ], "topics": [ "arithmetic" ] }, { "categories": [ "en:Set theory" ], "examples": [ { "text": "1950, Frederick Bagemihl (translator), Erich Kamke, Theory of Sets, Dover (Dover Phoenix), 2006, page 137,\nFor 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." }, { "text": "1960 [D. Van Nostrand], Paul R. Halmos, Naive Set Theory, 2017, Dover, Republication, page 80,\nIs 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." }, { "text": "2009, Marek Kuczma, Attila Gilányi (editor), An Introduction to the Theory of Functional Equations and Inequalities, Springer (Birkhäuser), 2nd Edition, page 10,\nIf α is an ordinal number, then by definition any two well-ordered sets of type α 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 α we may assign a cardinal number, the common cardinality of all well-ordered sets of type α." } ], "glosses": [ "Such 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\"." ], "links": [ [ "set theory", "set theory" ], [ "cardinal number", "cardinal number" ], [ "set", "set" ], [ "order type", "order type" ], [ "well-ordered", "well-ordered" ], [ "cardinality", "cardinality" ], [ "equivalence class", "equivalence class" ], [ "equivalence relation", "equivalence relation" ], [ "bijection", "bijection" ] ], "raw_glosses": [ "(set theory) Such 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\"." ], "topics": [ "mathematics", "sciences", "set-theory" ] } ], "sounds": [ { "audio": "LL-Q1860 (eng)-Vealhurl-ordinal number.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav/LL-Q1860_%28eng%29-Vealhurl-ordinal_number.wav.ogg" } ], "synonyms": [ { "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "ordinal" }, { "topics": [ "grammar", "linguistics", "human-sciences", "sciences" ], "word": "ordinal numeral" }, { "topics": [ "arithmetic" ], "word": "ordinal" }, { "topics": [ "order-theory", "mathematics", "sciences" ], "word": "ordinal" } ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "nombre ordinal" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "順序數" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "shùnxùshù", "sense": "grammar: word used to denote relative position in a sequence", "word": "顺序数" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "序數" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshù", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "grammar: word used to denote relative position in a sequence", "word": "序數詞" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshùcí", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数词" }, { "code": "crh", "lang": "Crimean Tatar", "sense": "grammar: word used to denote relative position in a sequence", "word": "sıra sayısı" }, { "code": "cs", "lang": "Czech", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "řadová číslovka" }, { "code": "da", "lang": "Danish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordinaltal" }, { "code": "da", "lang": "Danish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordenstal" }, { "code": "nl", "lang": "Dutch", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "rangtelwoord" }, { "code": "fo", "lang": "Faroese", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "raðtal" }, { "code": "fi", "lang": "Finnish", "sense": "grammar: word used to denote relative position in a sequence", "word": "järjestyslukusana" }, { "code": "fi", "lang": "Finnish", "sense": "grammar: word used to denote relative position in a sequence", "word": "ordinaalilukusana" }, { "code": "fr", "lang": "French", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "nombre ordinal (pl. nombres ordinaux)" }, { "code": "gl", "lang": "Galician", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "número ordinal" }, { "code": "ka", "lang": "Georgian", "roman": "rigobiti ricxviti saxeli", "sense": "grammar: word used to denote relative position in a sequence", "word": "რიგობითი რიცხვითი სახელი" }, { "code": "ka", "lang": "Georgian", "roman": "rigiti ricxviti saxeli", "sense": "grammar: word used to denote relative position in a sequence", "word": "რიგითი რიცხვითი სახელი" }, { "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "Ordnungszahl" }, { "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "Ordnungszahlwort" }, { "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "Ordinale" }, { "code": "de", "lang": "German", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "Ordinalzahl" }, { "code": "el", "lang": "Greek", "roman": "taktikó arithmitikó", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "τακτικό αριθμητικό" }, { "code": "hi", "lang": "Hindi", "roman": "karmvācak saṅkhyā", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "कर्मवाचक संख्या" }, { "code": "hu", "lang": "Hungarian", "sense": "grammar: word used to denote relative position in a sequence", "word": "sorszámnév" }, { "code": "is", "lang": "Icelandic", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "raðtala" }, { "alt": "じょすうし", "code": "ja", "lang": "Japanese", "roman": "josūshi", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数詞" }, { "alt": "じょすう", "code": "ja", "lang": "Japanese", "roman": "josū", "sense": "grammar: word used to denote relative position in a sequence", "word": "序数" }, { "code": "ko", "lang": "Korean", "roman": "seosu", "sense": "grammar: word used to denote relative position in a sequence", "word": "서수" }, { "code": "ko", "lang": "Korean", "roman": "seosusa", "sense": "grammar: word used to denote relative position in a sequence", "word": "서수사" }, { "code": "nb", "lang": "Norwegian Bokmål", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "ordenstall" }, { "code": "pl", "lang": "Polish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "inanimate", "masculine" ], "word": "liczebnik porządkowy" }, { "code": "pl", "lang": "Polish", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "code": "pt", "lang": "Portuguese", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "número ordinal" }, { "code": "ru", "lang": "Russian", "roman": "porjádkovoje čislítelʹnoje", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "neuter" ], "word": "поря́дковое числи́тельное" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "grammar: word used to denote relative position in a sequence", "word": "redni broj" }, { "code": "sv", "lang": "Swedish", "sense": "grammar: word used to denote relative position in a sequence", "word": "ordningstal" }, { "code": "cy", "lang": "Welsh", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "trefnolyn" }, { "code": "cy", "lang": "Welsh", "sense": "grammar: word used to denote relative position in a sequence", "tags": [ "masculine" ], "word": "rhif trefnol" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "arithmetic: number used to denote position in a sequence", "word": "序數" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "xùshù", "sense": "arithmetic: number used to denote position in a sequence", "word": "序数" }, { "code": "fi", "lang": "Finnish", "sense": "arithmetic: number used to denote position in a sequence", "word": "järjestysluku" }, { "code": "fi", "lang": "Finnish", "sense": "arithmetic: number used to denote position in a sequence", "word": "ordinaaliluku" }, { "code": "mi", "lang": "Maori", "sense": "arithmetic: number used to denote position in a sequence", "word": "tau raupapa" }, { "code": "pl", "lang": "Polish", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "code": "ru", "lang": "Russian", "roman": "porjádkovyj nómer", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "поря́дковый но́мер" }, { "code": "ru", "lang": "Russian", "roman": "nómer", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "но́мер" }, { "code": "tl", "lang": "Tagalog", "sense": "arithmetic: number used to denote position in a sequence", "word": "bilang na panunod" }, { "code": "cy", "lang": "Welsh", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "trefnolyn" }, { "code": "cy", "lang": "Welsh", "sense": "arithmetic: number used to denote position in a sequence", "tags": [ "masculine" ], "word": "rhif trefnol" }, { "code": "cs", "lang": "Czech", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "neuter" ], "word": "ordinální číslo" }, { "code": "nl", "lang": "Dutch", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "neuter" ], "word": "ranggetal" }, { "code": "fi", "lang": "Finnish", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "ordinaali" }, { "code": "hu", "lang": "Hungarian", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "rendszám" }, { "alt": "じゅんじょすう", "code": "ja", "lang": "Japanese", "roman": "junjosū", "sense": "generalized kind of number to denote the length of a well-order on a set", "word": "順序数" }, { "code": "pl", "lang": "Polish", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "feminine" ], "word": "liczba porządkowa" }, { "code": "cy", "lang": "Welsh", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "masculine" ], "word": "trefnolyn" }, { "code": "cy", "lang": "Welsh", "sense": "generalized kind of number to denote the length of a well-order on a set", "tags": [ "masculine" ], "word": "rhif trefnol" } ], "wikipedia": [ "ordinal number" ], "word": "ordinal number" }
Download raw JSONL data for ordinal number meaning in English (16.3kB)
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