See bijection in All languages combined, or Wiktionary
Download JSON data for bijection meaning in English (8.8kB)
{
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"expansion": "PIE word\n *dwóh₁",
"name": "PIE word"
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"1": "en",
"2": "fr",
"3": "bijection"
},
"expansion": "French bijection",
"name": "bor"
}
],
"etymology_text": "PIE word\n *dwóh₁\nFrom French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.",
"forms": [
{
"form": "bijections",
"tags": [
"plural"
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"args": {},
"expansion": "bijection (plural bijections)",
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"lang_code": "en",
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{
"kind": "topical",
"langcode": "en",
"name": "Functions",
"orig": "en:Functions",
"parents": [
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"examples": [
{
"ref": "2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214",
"text": "The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.",
"type": "quotation"
},
{
"ref": "2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167",
"text": "Note in particular that a function is a bijection if and only if it's both an injection and a surjection.",
"type": "quotation"
},
{
"ref": "2013, William F. Basener, Topology and Its Applications, unnumbered page",
"text": "The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.",
"type": "quotation"
}
],
"glosses": [
"A one-to-one correspondence, a function which is both a surjection and an injection."
],
"id": "en-bijection-en-noun-xM4rpz94",
"links": [
[
"set theory",
"set theory"
],
[
"one-to-one",
"one-to-one"
],
[
"correspondence",
"correspondence"
],
[
"surjection",
"surjection"
],
[
"injection",
"injection"
]
],
"raw_glosses": [
"(set theory) A one-to-one correspondence, a function which is both a surjection and an injection."
],
"related": [
{
"word": "injection"
},
{
"word": "surjection"
}
],
"synonyms": [
{
"word": "bijective function"
},
{
"word": "one-to-one correspondence"
}
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funció bijectiva"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijecció"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yīyīyìngshè",
"sense": "function that is both a surjection and an injection",
"word": "一一映射"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "function that is both a surjection and an injection",
"word": "雙射"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shuāngshè",
"sense": "function that is both a surjection and an injection",
"word": "双射"
},
{
"code": "cs",
"lang": "Czech",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekce"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijectie"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "dissurĵeto"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "inversigebla funkcio"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "bijekcio"
},
{
"code": "et",
"lang": "Estonian",
"sense": "function that is both a surjection and an injection",
"word": "bijektsioon"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "function that is both a surjection and an injection",
"word": "bijektio"
},
{
"code": "fr",
"lang": "French",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijection"
},
{
"code": "de",
"lang": "German",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "Bijektion"
},
{
"code": "de",
"lang": "German",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijektive Funktion"
},
{
"code": "el",
"lang": "Greek",
"roman": "amfimonosímanti antistoichía",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "αμφιμονοσήμαντη αντιστοιχία"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "פונקציה חד-חד-ערכית ועל"
},
{
"code": "hi",
"lang": "Hindi",
"roman": "ekaikī ācchādan",
"sense": "function that is both a surjection and an injection",
"word": "एकैकी आच्छादन"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "function that is both a surjection and an injection",
"word": "bijekció"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "function that is both a surjection and an injection",
"word": "kölcsönösen egyértelmű leképezés"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "gagntæk vörpun"
},
{
"code": "io",
"lang": "Ido",
"sense": "function that is both a surjection and an injection",
"word": "bijekto"
},
{
"alt": "ぜんたんしゃ",
"code": "ja",
"lang": "Japanese",
"roman": "zentansha",
"sense": "function that is both a surjection and an injection",
"word": "全単射"
},
{
"alt": "そうしゃ",
"code": "ja",
"lang": "Japanese",
"roman": "sōsha",
"sense": "function that is both a surjection and an injection",
"word": "双射"
},
{
"code": "ko",
"lang": "Korean",
"roman": "jeondansa",
"sense": "function that is both a surjection and an injection",
"word": "전단사"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekcja"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funkcja wzajemnie jednoznaczna"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijeção"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijecție"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funcție bijectivă"
},
{
"code": "ru",
"lang": "Russian",
"roman": "bijékcija",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "бие́кция"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekcija"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "бијекција"
},
{
"code": "es",
"lang": "Spanish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "biyección"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "function that is both a surjection and an injection",
"tags": [
"common-gender"
],
"word": "bijektion"
}
],
"wikipedia": [
"Nicolas Bourbaki",
"bijection",
"Éléments de mathématique"
]
}
],
"sounds": [
{
"ipa": "/baɪˈd͡ʒɛk.ʃən/"
}
],
"word": "bijection"
}
{
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"expansion": "*dwóh₁",
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"args": {
"1": "en",
"2": "dwóh₁"
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"expansion": "PIE word\n *dwóh₁",
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"1": "en",
"2": "fr",
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},
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"name": "bor"
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],
"etymology_text": "PIE word\n *dwóh₁\nFrom French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.",
"forms": [
{
"form": "bijections",
"tags": [
"plural"
]
}
],
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{
"args": {},
"expansion": "bijection (plural bijections)",
"name": "en-noun"
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"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "injection"
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{
"word": "surjection"
}
],
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"categories": [
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"Korean terms with redundant script codes",
"Mandarin terms with redundant transliterations",
"en:Functions",
"en:Set theory"
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"examples": [
{
"ref": "2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214",
"text": "The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.",
"type": "quotation"
},
{
"ref": "2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167",
"text": "Note in particular that a function is a bijection if and only if it's both an injection and a surjection.",
"type": "quotation"
},
{
"ref": "2013, William F. Basener, Topology and Its Applications, unnumbered page",
"text": "The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.",
"type": "quotation"
}
],
"glosses": [
"A one-to-one correspondence, a function which is both a surjection and an injection."
],
"links": [
[
"set theory",
"set theory"
],
[
"one-to-one",
"one-to-one"
],
[
"correspondence",
"correspondence"
],
[
"surjection",
"surjection"
],
[
"injection",
"injection"
]
],
"raw_glosses": [
"(set theory) A one-to-one correspondence, a function which is both a surjection and an injection."
],
"topics": [
"mathematics",
"sciences",
"set-theory"
],
"wikipedia": [
"Nicolas Bourbaki",
"bijection",
"Éléments de mathématique"
]
}
],
"sounds": [
{
"ipa": "/baɪˈd͡ʒɛk.ʃən/"
}
],
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{
"word": "bijective function"
},
{
"word": "one-to-one correspondence"
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funció bijectiva"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijecció"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yīyīyìngshè",
"sense": "function that is both a surjection and an injection",
"word": "一一映射"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "function that is both a surjection and an injection",
"word": "雙射"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shuāngshè",
"sense": "function that is both a surjection and an injection",
"word": "双射"
},
{
"code": "cs",
"lang": "Czech",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekce"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijectie"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "dissurĵeto"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "inversigebla funkcio"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "function that is both a surjection and an injection",
"word": "bijekcio"
},
{
"code": "et",
"lang": "Estonian",
"sense": "function that is both a surjection and an injection",
"word": "bijektsioon"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "function that is both a surjection and an injection",
"word": "bijektio"
},
{
"code": "fr",
"lang": "French",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijection"
},
{
"code": "de",
"lang": "German",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "Bijektion"
},
{
"code": "de",
"lang": "German",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijektive Funktion"
},
{
"code": "el",
"lang": "Greek",
"roman": "amfimonosímanti antistoichía",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "αμφιμονοσήμαντη αντιστοιχία"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "פונקציה חד-חד-ערכית ועל"
},
{
"code": "hi",
"lang": "Hindi",
"roman": "ekaikī ācchādan",
"sense": "function that is both a surjection and an injection",
"word": "एकैकी आच्छादन"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "function that is both a surjection and an injection",
"word": "bijekció"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "function that is both a surjection and an injection",
"word": "kölcsönösen egyértelmű leképezés"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "gagntæk vörpun"
},
{
"code": "io",
"lang": "Ido",
"sense": "function that is both a surjection and an injection",
"word": "bijekto"
},
{
"alt": "ぜんたんしゃ",
"code": "ja",
"lang": "Japanese",
"roman": "zentansha",
"sense": "function that is both a surjection and an injection",
"word": "全単射"
},
{
"alt": "そうしゃ",
"code": "ja",
"lang": "Japanese",
"roman": "sōsha",
"sense": "function that is both a surjection and an injection",
"word": "双射"
},
{
"code": "ko",
"lang": "Korean",
"roman": "jeondansa",
"sense": "function that is both a surjection and an injection",
"word": "전단사"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekcja"
},
{
"code": "pl",
"lang": "Polish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funkcja wzajemnie jednoznaczna"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijeção"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijecție"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "funcție bijectivă"
},
{
"code": "ru",
"lang": "Russian",
"roman": "bijékcija",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "бие́кция"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "bijekcija"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "бијекција"
},
{
"code": "es",
"lang": "Spanish",
"sense": "function that is both a surjection and an injection",
"tags": [
"feminine"
],
"word": "biyección"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "function that is both a surjection and an injection",
"tags": [
"common-gender"
],
"word": "bijektion"
}
],
"word": "bijection"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-06 from the enwiktionary dump dated 2024-05-02 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.