See factorial in All languages combined, or Wiktionary
Download JSON data for factorial meaning in English (12.4kB)
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"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.",
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"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;1.2.3#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!",
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"tags": [
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},
{
"code": "is",
"english": "a factorial number",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"tags": [
"feminine"
],
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},
{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm hrópmerkt"
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{
"code": "is",
"english": "factorial of five",
"lang": "Icelandic",
"sense": "mathematical operation or its result",
"word": "fimm aðfaldað"
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"sense": "mathematical operation or its result",
"word": "階乗"
},
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"lang": "Korean",
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"sense": "mathematical operation or its result",
"word": "계승"
},
{
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"sense": "mathematical operation or its result",
"word": "факториал"
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"word": "huarea"
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{
"code": "nb",
"lang": "Norwegian Bokmål",
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"tags": [
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"word": "factorial"
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{
"code": "pl",
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"sense": "mathematical operation or its result",
"tags": [
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"sense": "mathematical operation or its result",
"tags": [
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"word": "factorial"
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{
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"sense": "mathematical operation or its result",
"word": "факториа́л"
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"word": "factorial"
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{
"code": "tl",
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"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"
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{
"code": "vi",
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"sense": "mathematical operation or its result",
"word": "giai thừa"
}
]
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{
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"form": "more factorial",
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"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.(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": "quotation"
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"ref": "1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, 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": "quotation"
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],
"id": "en-factorial-en-adj-fsrINKni",
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"(mathematics) Of or pertaining to a factor or factorial."
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{
"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": "quotation"
}
],
"glosses": [
"Of or pertaining to a factor, a kind of business agent."
],
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],
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"(dated) Of or pertaining to a factory."
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"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.",
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"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;1.2.3#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!",
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],
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"sense": "mathematical operation or its result",
"word": "ֆակտորիալ"
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],
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{
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"sense": "mathematical operation or its result",
"word": "階乘"
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{
"code": "cmn",
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"sense": "mathematical operation or its result",
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"tags": [
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"word": "fakultet"
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"word": "kertoma"
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"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": "factorial"
},
{
"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": [
"masculine"
],
"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 4-syllable words",
"English adjectives",
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English nouns",
"English terms suffixed with -ial",
"English terms with IPA pronunciation",
"English terms with audio links",
"es:Combinatorics"
],
"derived": [
{
"word": "factorial experiment"
},
{
"word": "factorial table"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "factor",
"3": "ial"
},
"expansion": "factor + -ial",
"name": "suffix"
}
],
"etymology_text": "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.(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": "quotation"
},
{
"ref": "1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, 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": "quotation"
}
],
"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": "quotation"
}
],
"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",
"tags": [
"Southern-England"
],
"text": "Audio (Southern England)"
}
],
"word": "factorial"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-01 from the enwiktionary dump dated 2024-04-21 using wiktextract (f4fd8c9 and c9440ce). 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.