See factorial on Wiktionary
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "factor",
"3": "ial"
},
"expansion": "factor + -ial",
"name": "suffix"
}
],
"etymology_text": "From factor + -ial.",
"forms": [
{
"form": "factorials",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial (plural factorials)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Combinatorics",
"orig": "en:Combinatorics",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Functions",
"orig": "en:Functions",
"parents": [
"Algebra",
"Calculus",
"Geometry",
"Mathematical analysis",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "13 3 12 72",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "14 0 4 82",
"kind": "other",
"name": "English terms suffixed with -ial",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 0 3 89",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 4 7 82",
"kind": "other",
"name": "Terms with Armenian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 5 7 80",
"kind": "other",
"name": "Terms with Bulgarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 4 7 80",
"kind": "other",
"name": "Terms with Catalan translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 3 13 73",
"kind": "other",
"name": "Terms with Czech translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "6 3 5 87",
"kind": "other",
"name": "Terms with Danish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "12 0 3 85",
"kind": "other",
"name": "Terms with Dutch translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 0 2 89",
"kind": "other",
"name": "Terms with Esperanto translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 4 7 80",
"kind": "other",
"name": "Terms with Estonian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 0 2 88",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 78",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "13 0 18 69",
"kind": "other",
"name": "Terms with Greek translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "7 4 15 75",
"kind": "other",
"name": "Terms with Hebrew translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 3 20 68",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Icelandic translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Irish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 0 3 87",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 0 3 87",
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Korean translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Kyrgyz translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 4 13 74",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Maori translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 77",
"kind": "other",
"name": "Terms with Norwegian Bokmål translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "6 2 3 89",
"kind": "other",
"name": "Terms with Norwegian Nynorsk translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 4 7 80",
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 4 6 81",
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "10 0 3 87",
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 0 2 90",
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 5 7 80",
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "9 5 8 79",
"kind": "other",
"name": "Terms with Tagalog translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "7 4 6 83",
"kind": "other",
"name": "Terms with Thai translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "7 5 7 82",
"kind": "other",
"name": "Terms with Turkish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "8 4 7 80",
"kind": "other",
"name": "Terms with Vietnamese translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428:",
"text": "The expression #x7B;#x7D;#x5F;nC#x5F;r means the number of combinations of n things taken r at a time. It is also written #x5C;binomnr, and is equal to#x5C;frac#x7B;n(n-1)(n-2)(n-3)#x5C;cdots#x5C;cdots(n-r#x2B;1)#x7D;#x7B;r#x21;#x7D;or n#x21;#x2F;r#x21;(n-r)#x21;, in which r#x21; is read \"factorial r\" and denotes the product of all the integral numbers from 1 to r inclusive.",
"type": "quote"
},
{
"ref": "2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School, volume 47, number 4, page 40:",
"text": "This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;1#x5C;cdot 2#x5C;cdot 3#x5C;cdotsn.But what does this equal?\nWell, of course we can say that it is equal to n factorial and write#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;n#x21; and then use our calculators, but inventing a new symbol like 'factorial' feels like an admission of defeat!",
"type": "quote"
}
],
"glosses": [
"The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120."
],
"hyponyms": [
{
"word": "double factorial"
},
{
"word": "falling factorial"
},
{
"word": "rising factorial"
}
],
"id": "en-factorial-en-noun-qCSV1WGG",
"links": [
[
"mathematics",
"mathematics"
],
[
"combinatorics",
"combinatorics"
]
],
"raw_glosses": [
"(mathematics, combinatorics) The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120."
],
"related": [
{
"word": "fact"
},
{
"word": "faction"
},
{
"word": "factor"
},
{
"word": "factorial prime"
},
{
"word": "factory"
},
{
"word": "fashion"
}
],
"topics": [
"combinatorics",
"mathematics",
"sciences"
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "faktorial",
"sense": "mathematical operation or its result",
"word": "ֆակտորիալ"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "faktoriál",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "факториа́л"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "factorial"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "mathematical operation or its result",
"word": "階乘"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "jiēchéng",
"sense": "mathematical operation or its result",
"word": "阶乘"
},
{
"code": "cs",
"lang": "Czech",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "faktoriál"
},
{
"code": "da",
"lang": "Danish",
"sense": "mathematical operation or its result",
"word": "fakultet"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "faculteit"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "mathematical operation or its result",
"word": "faktorialo"
},
{
"code": "et",
"lang": "Estonian",
"sense": "mathematical operation or its result",
"word": "faktoriaal"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "mathematical operation or its result",
"word": "kertoma"
},
{
"code": "fr",
"lang": "French",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "factorielle"
},
{
"code": "de",
"lang": "German",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "Fakultät"
},
{
"code": "el",
"lang": "Greek",
"roman": "paragontikó",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "παραγοντικό"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "'atzerét",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "עֲצֶרֶת"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "mathematical operation or its result",
"word": "faktoriális"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "aðfeldi"
},
{
"code": "is",
"english": "a factorial number",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "hrópmerkt tala"
},
{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm hrópmerkt"
},
{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm aðfaldað"
},
{
"code": "ga",
"lang": "Irish",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "iolrán"
},
{
"code": "it",
"lang": "Italian",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "fattoriale"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kaijō",
"sense": "mathematical operation or its result",
"word": "階乗"
},
{
"code": "ko",
"lang": "Korean",
"roman": "gyeseung",
"sense": "mathematical operation or its result",
"word": "계승"
},
{
"code": "ky",
"lang": "Kyrgyz",
"roman": "faktorial",
"sense": "mathematical operation or its result",
"word": "факториал"
},
{
"code": "mi",
"lang": "Maori",
"sense": "mathematical operation or its result",
"word": "huarea"
},
{
"code": "nb",
"lang": "Norwegian Bokmål",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "fakultet"
},
{
"code": "nn",
"lang": "Norwegian Nynorsk",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "fakultet"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "silnia"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematical operation or its result",
"tags": [
"dated",
"masculine"
],
"word": "faktoriał"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "fatorial"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "factorial"
},
{
"code": "ru",
"lang": "Russian",
"roman": "faktoriál",
"sense": "mathematical operation or its result",
"word": "факториа́л"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "factorial"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematical operation or its result",
"tags": [
"common-gender"
],
"word": "fakultet"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "mathematical operation or its result",
"word": "buuin"
},
{
"code": "th",
"lang": "Thai",
"sense": "mathematical operation or its result",
"word": "แฟกทอเรียล"
},
{
"code": "tr",
"lang": "Turkish",
"sense": "mathematical operation or its result",
"word": "faktöriyel"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "mathematical operation or its result",
"word": "giai thừa"
}
]
}
],
"sounds": [
{
"ipa": "/fækˈtɔːɹi.əl/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-factorial.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.ogg"
},
{
"rhymes": "-ɔːɹiəl"
}
],
"word": "factorial"
}
{
"derived": [
{
"_dis1": "0 0 0",
"word": "factorial experiment"
},
{
"_dis1": "0 0 0",
"word": "factorial table"
},
{
"_dis1": "0 0 0",
"word": "monofactorial"
},
{
"_dis1": "0 0 0",
"word": "polyfactorial"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "factor",
"3": "ial"
},
"expansion": "factor + -ial",
"name": "suffix"
}
],
"etymology_text": "From factor + -ial.",
"forms": [
{
"form": "more factorial",
"tags": [
"comparative"
]
},
{
"form": "most factorial",
"tags": [
"superlative"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial (comparative more factorial, superlative most factorial)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"_dis1": "0 0 0",
"word": "primorial"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "1903, Arthur Schuster, “On some Definite Integrals, and a New Method of Reducing a Function of Spherical Co-ordintes to a Series of Spherical Harmonics”, in Philosophical Transactions of the Royal Society A, volume 200, →DOI, →JSTOR, page 182:",
"text": "I shall denote, as usual, the factorial product of the numbers up to n by n#x21;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#x21;#x21;#x3D;n#x5C;cdot(n-2)#x21;#x21;.Starting with1#x21;#x21;#x3D;1,#x5C;quad 2#x21;#x21;#x3D;2,it follows that, for positive values of n,n#x21;#x21;#x3D;n#x5C;cdotn-2#x5C;cdotn-4#x5C;cdots,where the last factor is either 1 or 2, according as n is odd or even.",
"type": "quote"
},
{
"ref": "1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, →ISBN, page 21:",
"text": "The definition of addition is an example of definition by induction, sometimes called recursive definition. As another example of this, consider the following inductive definition of the factorial function.\nWe define n#x21; for n#x5C;in#x5C;mathbbN by the following two properties,\n(i) 1#x21; is defined to be 1,\n(ii) for all k#x5C;in#x5C;mathbbN, we define (k#x2B;1)#x21; to be (k#x2B;1)#x5C;timesk#x21;.",
"type": "quote"
}
],
"glosses": [
"Of or pertaining to a factor or factorial."
],
"id": "en-factorial-en-adj-fsrINKni",
"links": [
[
"mathematics",
"mathematics"
],
[
"factor",
"factor"
],
[
"factorial",
"factorial#Noun"
]
],
"raw_glosses": [
"(mathematics) Of or pertaining to a factor or factorial."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [],
"examples": [
{
"ref": "2004, The Digest: Annotated British, Commonwealth, and European Cases:",
"text": "The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted.",
"type": "quote"
}
],
"glosses": [
"Of or pertaining to a factor, a kind of business agent."
],
"id": "en-factorial-en-adj-KYFtiBmo",
"links": [
[
"factor",
"factor"
]
]
},
{
"categories": [],
"glosses": [
"Of or pertaining to a factory."
],
"id": "en-factorial-en-adj-TvC7CtCD",
"links": [
[
"factory",
"factory"
]
],
"raw_glosses": [
"(dated) Of or pertaining to a factory."
],
"tags": [
"dated"
]
}
],
"sounds": [
{
"ipa": "/fækˈtɔːɹi.əl/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-factorial.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.ogg"
},
{
"rhymes": "-ɔːɹiəl"
}
],
"word": "factorial"
}
{
"forms": [
{
"form": "factoriais",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "m"
},
"expansion": "factorial m (plural factoriais)",
"name": "pt-noun"
}
],
"lang": "Portuguese",
"lang_code": "pt",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "European Portuguese forms superseded by AO1990",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Portuguese forms superseded in 1943",
"parents": [],
"source": "w"
},
{
"_dis": "50 50",
"kind": "other",
"name": "Portuguese entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"glosses": [
"Pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling."
],
"id": "en-factorial-pt-noun-QeROU0Fp",
"links": [
[
"fatorial",
"fatorial#Portuguese"
]
],
"tags": [
"masculine"
]
}
],
"word": "factorial"
}
{
"forms": [
{
"form": "factoriais",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or f (plural factoriais)",
"name": "pt-adj"
}
],
"lang": "Portuguese",
"lang_code": "pt",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "European Portuguese forms superseded by AO1990",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Portuguese forms superseded in 1943",
"parents": [],
"source": "w"
},
{
"_dis": "50 50",
"kind": "other",
"name": "Portuguese entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"glosses": [
"Pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling."
],
"id": "en-factorial-pt-adj-QeROU0Fp",
"links": [
[
"fatorial",
"fatorial#Portuguese"
]
],
"tags": [
"feminine",
"masculine"
]
}
],
"word": "factorial"
}
{
"etymology_templates": [
{
"args": {
"1": "ro",
"2": "fr",
"3": "factorielle"
},
"expansion": "Borrowed from French factorielle",
"name": "bor+"
}
],
"etymology_text": "Borrowed from French factorielle.",
"forms": [
{
"form": "factorială",
"tags": [
"feminine",
"singular"
]
},
{
"form": "factoriali",
"tags": [
"masculine",
"plural"
]
},
{
"form": "factoriale",
"tags": [
"feminine",
"neuter",
"plural"
]
},
{
"form": "no-table-tags",
"source": "declension",
"tags": [
"table-tags"
]
},
{
"form": "ro-decl-adj",
"source": "declension",
"tags": [
"inflection-template"
]
},
{
"form": "factorial",
"source": "declension",
"tags": [
"error-unrecognized-form",
"indefinite",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factorială",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"singular"
]
},
{
"form": "factoriali",
"source": "declension",
"tags": [
"error-unrecognized-form",
"indefinite",
"masculine",
"plural"
]
},
{
"form": "factoriale",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"neuter",
"plural"
]
},
{
"form": "factorialul",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factoriala",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"singular"
]
},
{
"form": "factorialii",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"plural"
]
},
{
"form": "factorialele",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"neuter",
"plural"
]
},
{
"form": "factoriale",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"singular"
]
},
{
"form": "factorialului",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factorialei",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"singular"
]
},
{
"form": "factorialilor",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"plural"
]
},
{
"form": "factorialelor",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"neuter",
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or n (feminine singular factorială, masculine plural factoriali, feminine and neuter plural factoriale)",
"name": "ro-adj"
}
],
"inflection_templates": [
{
"args": {},
"name": "ro-decl-adj"
}
],
"lang": "Romanian",
"lang_code": "ro",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "Pages with 4 entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Romanian entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"_dis": "2 0 1 16 19 19 41 0 3",
"kind": "other",
"name": "Pages with 4 entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "1 0 0 14 23 22 37 0 2",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"factorial"
],
"id": "en-factorial-ro-adj-BJsyU~So",
"links": [
[
"factorial",
"factorial#English"
]
],
"tags": [
"masculine",
"neuter"
]
}
],
"word": "factorial"
}
{
"etymology_templates": [
{
"args": {
"1": "es",
"2": "fr",
"3": "factorielle"
},
"expansion": "French factorielle",
"name": "bor"
},
{
"args": {
"1": "es",
"2": "factor",
"3": "-al"
},
"expansion": "factor + -al",
"name": "af"
}
],
"etymology_text": "From French factorielle. Equivalent to factor + -al.",
"forms": [
{
"form": "factoriales",
"tags": [
"feminine",
"masculine",
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or f (masculine and feminine plural factoriales)",
"name": "es-adj"
}
],
"hyphenation": [
"fac‧to‧rial"
],
"lang": "Spanish",
"lang_code": "es",
"pos": "adj",
"senses": [
{
"derived": [
{
"word": "análisis factorial"
}
],
"glosses": [
"factorial"
],
"id": "en-factorial-es-adj-BJsyU~So",
"links": [
[
"factorial",
"factorial#English"
]
],
"tags": [
"feminine",
"masculine"
]
}
],
"sounds": [
{
"ipa": "/faɡtoˈɾjal/"
},
{
"ipa": "[faɣ̞.t̪oˈɾjal]"
},
{
"rhymes": "-al"
}
],
"word": "factorial"
}
{
"etymology_templates": [
{
"args": {
"1": "es",
"2": "fr",
"3": "factorielle"
},
"expansion": "French factorielle",
"name": "bor"
},
{
"args": {
"1": "es",
"2": "factor",
"3": "-al"
},
"expansion": "factor + -al",
"name": "af"
}
],
"etymology_text": "From French factorielle. Equivalent to factor + -al.",
"forms": [
{
"form": "factoriales",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "m"
},
"expansion": "factorial m (plural factoriales)",
"name": "es-noun"
}
],
"hyphenation": [
"fac‧to‧rial"
],
"lang": "Spanish",
"lang_code": "es",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "es",
"name": "Mathematics",
"orig": "es:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "4 96",
"kind": "other",
"name": "Spanish entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "0 100",
"kind": "other",
"name": "Spanish terms suffixed with -al",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "0 100",
"kind": "topical",
"langcode": "es",
"name": "Combinatorics",
"orig": "es:Combinatorics",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"glosses": [
"factorial"
],
"id": "en-factorial-es-noun-BJsyU~So",
"links": [
[
"mathematics",
"mathematics"
],
[
"factorial",
"factorial#English"
]
],
"raw_glosses": [
"(mathematics) factorial"
],
"tags": [
"masculine"
],
"topics": [
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/faɡtoˈɾjal/"
},
{
"ipa": "[faɣ̞.t̪oˈɾjal]"
},
{
"rhymes": "-al"
}
],
"word": "factorial"
}
{
"categories": [
"English adjectives",
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English nouns",
"English terms suffixed with -ial",
"Entries with translation boxes",
"Pages with 4 entries",
"Pages with entries",
"Rhymes:English/ɔːɹiəl",
"Rhymes:English/ɔːɹiəl/4 syllables",
"Terms with Armenian translations",
"Terms with Bulgarian translations",
"Terms with Catalan translations",
"Terms with Czech translations",
"Terms with Danish translations",
"Terms with Dutch translations",
"Terms with Esperanto translations",
"Terms with Estonian translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Greek translations",
"Terms with Hebrew 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 Kyrgyz 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 Spanish translations",
"Terms with Swedish translations",
"Terms with Tagalog translations",
"Terms with Thai translations",
"Terms with Turkish translations",
"Terms with Vietnamese translations",
"es:Combinatorics"
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "factor",
"3": "ial"
},
"expansion": "factor + -ial",
"name": "suffix"
}
],
"etymology_text": "From factor + -ial.",
"forms": [
{
"form": "factorials",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial (plural factorials)",
"name": "en-noun"
}
],
"hyponyms": [
{
"word": "double factorial"
},
{
"word": "falling factorial"
},
{
"word": "rising factorial"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "fact"
},
{
"word": "faction"
},
{
"word": "factor"
},
{
"word": "factorial prime"
},
{
"word": "factory"
},
{
"word": "fashion"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Combinatorics",
"en:Functions",
"en:Mathematics"
],
"examples": [
{
"ref": "1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428:",
"text": "The expression #x7B;#x7D;#x5F;nC#x5F;r means the number of combinations of n things taken r at a time. It is also written #x5C;binomnr, and is equal to#x5C;frac#x7B;n(n-1)(n-2)(n-3)#x5C;cdots#x5C;cdots(n-r#x2B;1)#x7D;#x7B;r#x21;#x7D;or n#x21;#x2F;r#x21;(n-r)#x21;, in which r#x21; is read \"factorial r\" and denotes the product of all the integral numbers from 1 to r inclusive.",
"type": "quote"
},
{
"ref": "2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School, volume 47, number 4, page 40:",
"text": "This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;1#x5C;cdot 2#x5C;cdot 3#x5C;cdotsn.But what does this equal?\nWell, of course we can say that it is equal to n factorial and write#x5C;prod#x5F;#x7B;k#x3D;1#x7D;ⁿk#x3D;n#x21; and then use our calculators, but inventing a new symbol like 'factorial' feels like an admission of defeat!",
"type": "quote"
}
],
"glosses": [
"The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"combinatorics",
"combinatorics"
]
],
"raw_glosses": [
"(mathematics, combinatorics) The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120."
],
"topics": [
"combinatorics",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/fækˈtɔːɹi.əl/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-factorial.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.ogg"
},
{
"rhymes": "-ɔːɹiəl"
}
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "faktorial",
"sense": "mathematical operation or its result",
"word": "ֆակտորիալ"
},
{
"code": "bg",
"lang": "Bulgarian",
"roman": "faktoriál",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "факториа́л"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "factorial"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "mathematical operation or its result",
"word": "階乘"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "jiēchéng",
"sense": "mathematical operation or its result",
"word": "阶乘"
},
{
"code": "cs",
"lang": "Czech",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "faktoriál"
},
{
"code": "da",
"lang": "Danish",
"sense": "mathematical operation or its result",
"word": "fakultet"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "faculteit"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "mathematical operation or its result",
"word": "faktorialo"
},
{
"code": "et",
"lang": "Estonian",
"sense": "mathematical operation or its result",
"word": "faktoriaal"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "mathematical operation or its result",
"word": "kertoma"
},
{
"code": "fr",
"lang": "French",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "factorielle"
},
{
"code": "de",
"lang": "German",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "Fakultät"
},
{
"code": "el",
"lang": "Greek",
"roman": "paragontikó",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "παραγοντικό"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "'atzerét",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "עֲצֶרֶת"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "mathematical operation or its result",
"word": "faktoriális"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "aðfeldi"
},
{
"code": "is",
"english": "a factorial number",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "hrópmerkt tala"
},
{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm hrópmerkt"
},
{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm aðfaldað"
},
{
"code": "ga",
"lang": "Irish",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "iolrán"
},
{
"code": "it",
"lang": "Italian",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "fattoriale"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kaijō",
"sense": "mathematical operation or its result",
"word": "階乗"
},
{
"code": "ko",
"lang": "Korean",
"roman": "gyeseung",
"sense": "mathematical operation or its result",
"word": "계승"
},
{
"code": "ky",
"lang": "Kyrgyz",
"roman": "faktorial",
"sense": "mathematical operation or its result",
"word": "факториал"
},
{
"code": "mi",
"lang": "Maori",
"sense": "mathematical operation or its result",
"word": "huarea"
},
{
"code": "nb",
"lang": "Norwegian Bokmål",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "fakultet"
},
{
"code": "nn",
"lang": "Norwegian Nynorsk",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "fakultet"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
"word": "silnia"
},
{
"code": "pl",
"lang": "Polish",
"sense": "mathematical operation or its result",
"tags": [
"dated",
"masculine"
],
"word": "faktoriał"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "fatorial"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "mathematical operation or its result",
"tags": [
"neuter"
],
"word": "factorial"
},
{
"code": "ru",
"lang": "Russian",
"roman": "faktoriál",
"sense": "mathematical operation or its result",
"word": "факториа́л"
},
{
"code": "es",
"lang": "Spanish",
"sense": "mathematical operation or its result",
"tags": [
"masculine"
],
"word": "factorial"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "mathematical operation or its result",
"tags": [
"common-gender"
],
"word": "fakultet"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "mathematical operation or its result",
"word": "buuin"
},
{
"code": "th",
"lang": "Thai",
"sense": "mathematical operation or its result",
"word": "แฟกทอเรียล"
},
{
"code": "tr",
"lang": "Turkish",
"sense": "mathematical operation or its result",
"word": "faktöriyel"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "mathematical operation or its result",
"word": "giai thừa"
}
],
"word": "factorial"
}
{
"categories": [
"English adjectives",
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English nouns",
"English terms suffixed with -ial",
"Entries with translation boxes",
"Pages with 4 entries",
"Pages with entries",
"Rhymes:English/ɔːɹiəl",
"Rhymes:English/ɔːɹiəl/4 syllables",
"Terms with Armenian translations",
"Terms with Bulgarian translations",
"Terms with Catalan translations",
"Terms with Czech translations",
"Terms with Danish translations",
"Terms with Dutch translations",
"Terms with Esperanto translations",
"Terms with Estonian translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Greek translations",
"Terms with Hebrew 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 Kyrgyz 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 Spanish translations",
"Terms with Swedish translations",
"Terms with Tagalog translations",
"Terms with Thai translations",
"Terms with Turkish translations",
"Terms with Vietnamese translations",
"es:Combinatorics"
],
"derived": [
{
"word": "factorial experiment"
},
{
"word": "factorial table"
},
{
"word": "monofactorial"
},
{
"word": "polyfactorial"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "factor",
"3": "ial"
},
"expansion": "factor + -ial",
"name": "suffix"
}
],
"etymology_text": "From factor + -ial.",
"forms": [
{
"form": "more factorial",
"tags": [
"comparative"
]
},
{
"form": "most factorial",
"tags": [
"superlative"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial (comparative more factorial, superlative most factorial)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "primorial"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Mathematics"
],
"examples": [
{
"ref": "1903, Arthur Schuster, “On some Definite Integrals, and a New Method of Reducing a Function of Spherical Co-ordintes to a Series of Spherical Harmonics”, in Philosophical Transactions of the Royal Society A, volume 200, →DOI, →JSTOR, page 182:",
"text": "I shall denote, as usual, the factorial product of the numbers up to n by n#x21;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#x21;#x21;#x3D;n#x5C;cdot(n-2)#x21;#x21;.Starting with1#x21;#x21;#x3D;1,#x5C;quad 2#x21;#x21;#x3D;2,it follows that, for positive values of n,n#x21;#x21;#x3D;n#x5C;cdotn-2#x5C;cdotn-4#x5C;cdots,where the last factor is either 1 or 2, according as n is odd or even.",
"type": "quote"
},
{
"ref": "1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, →ISBN, page 21:",
"text": "The definition of addition is an example of definition by induction, sometimes called recursive definition. As another example of this, consider the following inductive definition of the factorial function.\nWe define n#x21; for n#x5C;in#x5C;mathbbN by the following two properties,\n(i) 1#x21; is defined to be 1,\n(ii) for all k#x5C;in#x5C;mathbbN, we define (k#x2B;1)#x21; to be (k#x2B;1)#x5C;timesk#x21;.",
"type": "quote"
}
],
"glosses": [
"Of or pertaining to a factor or factorial."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"factor",
"factor"
],
[
"factorial",
"factorial#Noun"
]
],
"raw_glosses": [
"(mathematics) Of or pertaining to a factor or factorial."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned"
],
"examples": [
{
"ref": "2004, The Digest: Annotated British, Commonwealth, and European Cases:",
"text": "The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted.",
"type": "quote"
}
],
"glosses": [
"Of or pertaining to a factor, a kind of business agent."
],
"links": [
[
"factor",
"factor"
]
]
},
{
"categories": [
"English dated terms"
],
"glosses": [
"Of or pertaining to a factory."
],
"links": [
[
"factory",
"factory"
]
],
"raw_glosses": [
"(dated) Of or pertaining to a factory."
],
"tags": [
"dated"
]
}
],
"sounds": [
{
"ipa": "/fækˈtɔːɹi.əl/"
},
{
"audio": "LL-Q1860 (eng)-Vealhurl-factorial.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/LL-Q1860_%28eng%29-Vealhurl-factorial.wav/LL-Q1860_%28eng%29-Vealhurl-factorial.wav.ogg"
},
{
"rhymes": "-ɔːɹiəl"
}
],
"word": "factorial"
}
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"Portuguese adjectives",
"Portuguese countable nouns",
"Portuguese entries with incorrect language header",
"Portuguese lemmas",
"Portuguese masculine nouns",
"Portuguese nouns",
"es:Combinatorics"
],
"forms": [
{
"form": "factoriais",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "m"
},
"expansion": "factorial m (plural factoriais)",
"name": "pt-noun"
}
],
"lang": "Portuguese",
"lang_code": "pt",
"pos": "noun",
"senses": [
{
"categories": [
"European Portuguese forms superseded by AO1990",
"Portuguese forms superseded in 1943"
],
"glosses": [
"Pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling."
],
"links": [
[
"fatorial",
"fatorial#Portuguese"
]
],
"tags": [
"masculine"
]
}
],
"word": "factorial"
}
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"Portuguese adjectives",
"Portuguese countable nouns",
"Portuguese entries with incorrect language header",
"Portuguese lemmas",
"Portuguese masculine nouns",
"Portuguese nouns",
"es:Combinatorics"
],
"forms": [
{
"form": "factoriais",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or f (plural factoriais)",
"name": "pt-adj"
}
],
"lang": "Portuguese",
"lang_code": "pt",
"pos": "adj",
"senses": [
{
"categories": [
"European Portuguese forms superseded by AO1990",
"Portuguese forms superseded in 1943"
],
"glosses": [
"Pre-reform spelling (used until 1943 in Brazil and 1990 in Portugal) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling."
],
"links": [
[
"fatorial",
"fatorial#Portuguese"
]
],
"tags": [
"feminine",
"masculine"
]
}
],
"word": "factorial"
}
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"es:Combinatorics"
],
"etymology_templates": [
{
"args": {
"1": "ro",
"2": "fr",
"3": "factorielle"
},
"expansion": "Borrowed from French factorielle",
"name": "bor+"
}
],
"etymology_text": "Borrowed from French factorielle.",
"forms": [
{
"form": "factorială",
"tags": [
"feminine",
"singular"
]
},
{
"form": "factoriali",
"tags": [
"masculine",
"plural"
]
},
{
"form": "factoriale",
"tags": [
"feminine",
"neuter",
"plural"
]
},
{
"form": "no-table-tags",
"source": "declension",
"tags": [
"table-tags"
]
},
{
"form": "ro-decl-adj",
"source": "declension",
"tags": [
"inflection-template"
]
},
{
"form": "factorial",
"source": "declension",
"tags": [
"error-unrecognized-form",
"indefinite",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factorială",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"singular"
]
},
{
"form": "factoriali",
"source": "declension",
"tags": [
"error-unrecognized-form",
"indefinite",
"masculine",
"plural"
]
},
{
"form": "factoriale",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"neuter",
"plural"
]
},
{
"form": "factorialul",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factoriala",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"singular"
]
},
{
"form": "factorialii",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"plural"
]
},
{
"form": "factorialele",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"neuter",
"plural"
]
},
{
"form": "factoriale",
"source": "declension",
"tags": [
"error-unrecognized-form",
"feminine",
"indefinite",
"singular"
]
},
{
"form": "factorialului",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"neuter",
"singular"
]
},
{
"form": "factorialei",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"singular"
]
},
{
"form": "factorialilor",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"masculine",
"plural"
]
},
{
"form": "factorialelor",
"source": "declension",
"tags": [
"definite",
"error-unrecognized-form",
"feminine",
"neuter",
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or n (feminine singular factorială, masculine plural factoriali, feminine and neuter plural factoriale)",
"name": "ro-adj"
}
],
"inflection_templates": [
{
"args": {},
"name": "ro-decl-adj"
}
],
"lang": "Romanian",
"lang_code": "ro",
"pos": "adj",
"senses": [
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"Romanian adjectives",
"Romanian entries with incorrect language header",
"Romanian lemmas",
"Romanian terms borrowed from French",
"Romanian terms derived from French"
],
"glosses": [
"factorial"
],
"links": [
[
"factorial",
"factorial#English"
]
],
"tags": [
"masculine",
"neuter"
]
}
],
"word": "factorial"
}
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"Rhymes:Spanish/al",
"Rhymes:Spanish/al/3 syllables",
"Spanish 3-syllable words",
"Spanish adjectives",
"Spanish countable nouns",
"Spanish entries with incorrect language header",
"Spanish epicene adjectives",
"Spanish lemmas",
"Spanish masculine nouns",
"Spanish nouns",
"Spanish terms borrowed from French",
"Spanish terms derived from French",
"Spanish terms suffixed with -al",
"Spanish terms with IPA pronunciation",
"es:Combinatorics"
],
"derived": [
{
"word": "análisis factorial"
}
],
"etymology_templates": [
{
"args": {
"1": "es",
"2": "fr",
"3": "factorielle"
},
"expansion": "French factorielle",
"name": "bor"
},
{
"args": {
"1": "es",
"2": "factor",
"3": "-al"
},
"expansion": "factor + -al",
"name": "af"
}
],
"etymology_text": "From French factorielle. Equivalent to factor + -al.",
"forms": [
{
"form": "factoriales",
"tags": [
"feminine",
"masculine",
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "factorial m or f (masculine and feminine plural factoriales)",
"name": "es-adj"
}
],
"hyphenation": [
"fac‧to‧rial"
],
"lang": "Spanish",
"lang_code": "es",
"pos": "adj",
"senses": [
{
"glosses": [
"factorial"
],
"links": [
[
"factorial",
"factorial#English"
]
],
"tags": [
"feminine",
"masculine"
]
}
],
"sounds": [
{
"ipa": "/faɡtoˈɾjal/"
},
{
"ipa": "[faɣ̞.t̪oˈɾjal]"
},
{
"rhymes": "-al"
}
],
"word": "factorial"
}
{
"categories": [
"Pages with 4 entries",
"Pages with entries",
"Rhymes:Spanish/al",
"Rhymes:Spanish/al/3 syllables",
"Spanish 3-syllable words",
"Spanish adjectives",
"Spanish countable nouns",
"Spanish entries with incorrect language header",
"Spanish epicene adjectives",
"Spanish lemmas",
"Spanish masculine nouns",
"Spanish nouns",
"Spanish terms borrowed from French",
"Spanish terms derived from French",
"Spanish terms suffixed with -al",
"Spanish terms with IPA pronunciation",
"es:Combinatorics"
],
"etymology_templates": [
{
"args": {
"1": "es",
"2": "fr",
"3": "factorielle"
},
"expansion": "French factorielle",
"name": "bor"
},
{
"args": {
"1": "es",
"2": "factor",
"3": "-al"
},
"expansion": "factor + -al",
"name": "af"
}
],
"etymology_text": "From French factorielle. Equivalent to factor + -al.",
"forms": [
{
"form": "factoriales",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "m"
},
"expansion": "factorial m (plural factoriales)",
"name": "es-noun"
}
],
"hyphenation": [
"fac‧to‧rial"
],
"lang": "Spanish",
"lang_code": "es",
"pos": "noun",
"senses": [
{
"categories": [
"es:Mathematics"
],
"glosses": [
"factorial"
],
"links": [
[
"mathematics",
"mathematics"
],
[
"factorial",
"factorial#English"
]
],
"raw_glosses": [
"(mathematics) factorial"
],
"tags": [
"masculine"
],
"topics": [
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/faɡtoˈɾjal/"
},
{
"ipa": "[faɣ̞.t̪oˈɾjal]"
},
{
"rhymes": "-al"
}
],
"word": "factorial"
}
Download raw JSONL data for factorial meaning in All languages combined (21.7kB)
{
"called_from": "inflection/735",
"msg": "inflection table: unrecognized header: 'nominative- accusative'",
"path": [
"factorial"
],
"section": "Romanian",
"subsection": "adjective",
"title": "factorial",
"trace": ""
}
{
"called_from": "inflection/735",
"msg": "inflection table: unrecognized header: 'nominative- accusative'",
"path": [
"factorial"
],
"section": "Romanian",
"subsection": "adjective",
"title": "factorial",
"trace": ""
}
{
"called_from": "inflection/735",
"msg": "inflection table: unrecognized header: 'genitive- dative'",
"path": [
"factorial"
],
"section": "Romanian",
"subsection": "adjective",
"title": "factorial",
"trace": ""
}
{
"called_from": "inflection/735",
"msg": "inflection table: unrecognized header: 'genitive- dative'",
"path": [
"factorial"
],
"section": "Romanian",
"subsection": "adjective",
"title": "factorial",
"trace": ""
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.