See codomain in All languages combined, or Wiktionary
Download JSON data for codomain meaning in English (6.6kB)
{
"antonyms": [
{
"sense": "antonym(s) of \"target set of a function\"",
"word": "domain"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "co",
"3": "domain"
},
"expansion": "co- + domain",
"name": "prefix"
}
],
"etymology_text": "co- + domain",
"forms": [
{
"form": "codomains",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "codomain (plural codomains)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"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"
}
],
"examples": [
{
"ref": "1994, Richard A. Holmgren, A First Course in Discrete Dynamical Systems, Springer, page 11",
"text": "Definition 2.5. A function is onto if each element of the codomain has at least one element of the domain assigned to it. In other words, a function is onto if the range equals the codomain.",
"type": "quotation"
},
{
"text": "2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Jones & Bartlett Learning, page 192,\nOnce we have described f as a function from A to B, by convention we will call B the codomain, even though other sets, of which B is a subset, could have been used. […] If y is an element of the codomain, then y∈ mathit Img(f,A) iff there is some x in the domain such that f maps x to y."
},
{
"ref": "2017, Alan Garfinkel, Jane Shevtsov, Yina Guo, Modeling Life: The Mathematics of Biological Systems, Springer, page 12",
"text": "For example, the codomain of g(X)#x3D;X³ consists of all real numbers. A function links each element in its domain to some element in its codomain. Each domain element is linked to exactly one codomain element.",
"type": "quotation"
}
],
"glosses": [
"The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y."
],
"id": "en-codomain-en-noun-7iHJTVYH",
"links": [
[
"mathematics",
"mathematics"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"function",
"function"
],
[
"domain",
"domain"
]
],
"raw_glosses": [
"(mathematics, mathematical analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"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": "40 60",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "21 79",
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "35 65",
"kind": "other",
"name": "English terms prefixed with co-",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "22 78",
"kind": "topical",
"langcode": "en",
"name": "Category theory",
"orig": "en:Category theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
},
{
"_dis": "29 71",
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w+disamb"
}
],
"glosses": [
"The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.",
"The set B."
],
"id": "en-codomain-en-noun-qcfqpUUt",
"links": [
[
"mathematics",
"mathematics"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"function",
"function"
],
[
"domain",
"domain"
],
[
"binary relation",
"binary relation"
]
],
"raw_glosses": [
"(mathematics, mathematical analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.",
"(more generally, of a binary relation R between A and B) The set B."
],
"raw_tags": [
"of a binary relation R between A and B"
],
"tags": [
"broadly"
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/ˌkoʊ.doʊˈmeɪn/",
"tags": [
"US"
]
},
{
"audio": "En-us-codomain.ogg",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/03/En-us-codomain.ogg/En-us-codomain.ogg.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/0/03/En-us-codomain.ogg",
"tags": [
"US"
],
"text": "Audio (US)"
}
],
"synonyms": [
{
"_dis1": "50 50",
"sense": "target set of a function",
"word": "range"
}
],
"translations": [
{
"_dis1": "50 50",
"code": "cs",
"lang": "Czech",
"sense": "target set of a function",
"tags": [
"masculine"
],
"word": "obor hodnot"
},
{
"_dis1": "50 50",
"code": "da",
"lang": "Danish",
"sense": "target set of a function",
"tags": [
"common-gender"
],
"word": "dispositionsmængde"
},
{
"_dis1": "50 50",
"code": "de",
"lang": "German",
"sense": "target set of a function",
"tags": [
"feminine"
],
"word": "Zielmenge"
},
{
"_dis1": "50 50",
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "aðmengi"
},
{
"_dis1": "50 50",
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "ítak"
},
{
"_dis1": "50 50",
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "bakmengi"
},
{
"_dis1": "50 50",
"alt": "しゅういき",
"code": "ja",
"lang": "Japanese",
"roman": "shūiki",
"sense": "target set of a function",
"word": "終域"
},
{
"_dis1": "50 50",
"code": "pl",
"lang": "Polish",
"sense": "target set of a function",
"tags": [
"feminine"
],
"word": "przeciwdziedzina"
},
{
"_dis1": "50 50",
"code": "pt",
"lang": "Portuguese",
"sense": "target set of a function",
"tags": [
"masculine"
],
"word": "contradomínio"
},
{
"_dis1": "50 50",
"code": "ru",
"lang": "Russian",
"sense": "target set of a function",
"word": "область значений"
},
{
"_dis1": "50 50",
"code": "sv",
"lang": "Swedish",
"sense": "target set of a function",
"tags": [
"common-gender"
],
"word": "målmängd"
}
],
"wikipedia": [
"codomain"
],
"word": "codomain"
}
{
"antonyms": [
{
"sense": "antonym(s) of \"target set of a function\"",
"word": "domain"
}
],
"categories": [
"English 3-syllable words",
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English nouns",
"English terms prefixed with co-",
"English terms with IPA pronunciation",
"English terms with audio links",
"en:Category theory",
"en:Set theory"
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "co",
"3": "domain"
},
"expansion": "co- + domain",
"name": "prefix"
}
],
"etymology_text": "co- + domain",
"forms": [
{
"form": "codomains",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "codomain (plural codomains)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"en:Mathematical analysis",
"en:Mathematics"
],
"examples": [
{
"ref": "1994, Richard A. Holmgren, A First Course in Discrete Dynamical Systems, Springer, page 11",
"text": "Definition 2.5. A function is onto if each element of the codomain has at least one element of the domain assigned to it. In other words, a function is onto if the range equals the codomain.",
"type": "quotation"
},
{
"text": "2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Jones & Bartlett Learning, page 192,\nOnce we have described f as a function from A to B, by convention we will call B the codomain, even though other sets, of which B is a subset, could have been used. […] If y is an element of the codomain, then y∈ mathit Img(f,A) iff there is some x in the domain such that f maps x to y."
},
{
"ref": "2017, Alan Garfinkel, Jane Shevtsov, Yina Guo, Modeling Life: The Mathematics of Biological Systems, Springer, page 12",
"text": "For example, the codomain of g(X)#x3D;X³ consists of all real numbers. A function links each element in its domain to some element in its codomain. Each domain element is linked to exactly one codomain element.",
"type": "quotation"
}
],
"glosses": [
"The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"function",
"function"
],
[
"domain",
"domain"
]
],
"raw_glosses": [
"(mathematics, mathematical analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"en:Mathematical analysis",
"en:Mathematics"
],
"glosses": [
"The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.",
"The set B."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"mathematical analysis",
"mathematical analysis"
],
[
"function",
"function"
],
[
"domain",
"domain"
],
[
"binary relation",
"binary relation"
]
],
"raw_glosses": [
"(mathematics, mathematical analysis) The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.",
"(more generally, of a binary relation R between A and B) The set B."
],
"raw_tags": [
"of a binary relation R between A and B"
],
"tags": [
"broadly"
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"ipa": "/ˌkoʊ.doʊˈmeɪn/",
"tags": [
"US"
]
},
{
"audio": "En-us-codomain.ogg",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/03/En-us-codomain.ogg/En-us-codomain.ogg.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/0/03/En-us-codomain.ogg",
"tags": [
"US"
],
"text": "Audio (US)"
}
],
"synonyms": [
{
"sense": "target set of a function",
"word": "range"
}
],
"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "target set of a function",
"tags": [
"masculine"
],
"word": "obor hodnot"
},
{
"code": "da",
"lang": "Danish",
"sense": "target set of a function",
"tags": [
"common-gender"
],
"word": "dispositionsmængde"
},
{
"code": "de",
"lang": "German",
"sense": "target set of a function",
"tags": [
"feminine"
],
"word": "Zielmenge"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "aðmengi"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "ítak"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "target set of a function",
"tags": [
"neuter"
],
"word": "bakmengi"
},
{
"alt": "しゅういき",
"code": "ja",
"lang": "Japanese",
"roman": "shūiki",
"sense": "target set of a function",
"word": "終域"
},
{
"code": "pl",
"lang": "Polish",
"sense": "target set of a function",
"tags": [
"feminine"
],
"word": "przeciwdziedzina"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "target set of a function",
"tags": [
"masculine"
],
"word": "contradomínio"
},
{
"code": "ru",
"lang": "Russian",
"sense": "target set of a function",
"word": "область значений"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "target set of a function",
"tags": [
"common-gender"
],
"word": "målmängd"
}
],
"wikipedia": [
"codomain"
],
"word": "codomain"
}
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.