See bijective on Wiktionary
{
"derived": [
{
"_dis1": "0 0",
"word": "bijective numeration"
},
{
"_dis1": "0 0",
"word": "bijectively"
},
{
"_dis1": "0 0",
"word": "nonbijective"
},
{
"_dis1": "0 0",
"word": "bijectivity"
}
],
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "bijective (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"_dis1": "0 0",
"word": "bijection"
},
{
"_dis1": "0 0",
"word": "injective"
},
{
"_dis1": "0 0",
"word": "surjective"
},
{
"_dis1": "0 0",
"word": "reversible"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "59 41",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "62 38",
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "63 37",
"kind": "other",
"name": "Pages with 2 entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "62 38",
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Catalan translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "68 32",
"kind": "other",
"name": "Terms with Czech translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "74 26",
"kind": "other",
"name": "Terms with Danish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "68 32",
"kind": "other",
"name": "Terms with Dutch translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "67 33",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "66 34",
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Irish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "71 29",
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "71 29",
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "71 29",
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "69 31",
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"text": "1987, James S. Royer, A Connotational Theory of Program Structure, Springer, LNCS 273, page 15,\nThen, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN. (Note: In this FORTRAN example, we could have omitted restrictions on I/O and instead used a computable, bijective, numerical coding for inputs and outputs to get another EN determined by FORTRAN.)"
},
{
"text": "1993, Susan Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society, CBMS, Regional Conference Series in Mathematics, Number 83, page 124,\nRecent experience indicates that for infinite-dimensional Hopf algebras, the “right” definition of Galois is to require that β be bijective."
},
{
"text": "2008, B. Aslan, M. T. Sakalli, E. Bulus, Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings, Joachim von zur Gathen, José Luis Imana, Çetin Kaya Koç (editors), Arithmetic of Finite Fields: 2nd International Workshop, Springer, LNCS 5130, page 131,\nGenerally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective S-boxes."
},
{
"ref": "2010, Kang Feng, Mengzhao Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Springer, page 39:",
"text": "An isomorphism is a bijective homomorphism.",
"type": "quote"
},
{
"text": "2012 [Introduction to Graph Theory, McGraw-Hill], Gary Chartrand, Ping Zhang, A First Course in Graph Theory, 2013, Dover, Revised and corrected republication, page 64,\nThe proof that isomorphism is an equivalence relation relies on three fundamental properties of bijective functions (functions that are one-to-one and onto): (1) every identity function is bijective, (2) the inverse of every bijective function is also bijective, (3) the composition of two bijective functions is bijective."
}
],
"glosses": [
"Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective."
],
"id": "en-bijective-en-adj-~aCPs5ed",
"links": [
[
"mathematics",
"mathematics"
],
[
"function",
"function"
],
[
"codomain",
"codomain"
],
[
"domain",
"domain"
],
[
"one-to-one",
"one-to-one"
],
[
"injective",
"injective"
],
[
"surjective",
"surjective"
]
],
"raw_glosses": [
"(mathematics, of a function) Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective."
],
"raw_tags": [
"of a function"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "93 7",
"code": "ca",
"lang": "Catalan",
"sense": "both injective and surjective",
"word": "bijectiu"
},
{
"_dis1": "93 7",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yīyīyìngshède",
"sense": "both injective and surjective",
"word": "一一映射的"
},
{
"_dis1": "93 7",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shuāngshède",
"sense": "both injective and surjective",
"word": "双射的"
},
{
"_dis1": "93 7",
"code": "cs",
"lang": "Czech",
"sense": "both injective and surjective",
"word": "bijektivní"
},
{
"_dis1": "93 7",
"code": "da",
"lang": "Danish",
"sense": "both injective and surjective",
"word": "bijektiv"
},
{
"_dis1": "93 7",
"code": "nl",
"lang": "Dutch",
"sense": "both injective and surjective",
"word": "bijectief"
},
{
"_dis1": "93 7",
"code": "fi",
"lang": "Finnish",
"sense": "both injective and surjective",
"word": "bijektiivinen"
},
{
"_dis1": "93 7",
"code": "fr",
"lang": "French",
"sense": "both injective and surjective",
"word": "bijectif"
},
{
"_dis1": "93 7",
"code": "de",
"lang": "German",
"sense": "both injective and surjective",
"word": "bijektiv"
},
{
"_dis1": "93 7",
"code": "de",
"lang": "German",
"sense": "both injective and surjective",
"word": "eineindeutig"
},
{
"_dis1": "93 7",
"code": "hu",
"lang": "Hungarian",
"sense": "both injective and surjective",
"word": "bijektív"
},
{
"_dis1": "93 7",
"code": "hu",
"lang": "Hungarian",
"sense": "both injective and surjective",
"word": "kölcsönösen egyértelmű"
},
{
"_dis1": "93 7",
"code": "ga",
"lang": "Irish",
"sense": "both injective and surjective",
"word": "détheilgeach"
},
{
"_dis1": "93 7",
"code": "it",
"lang": "Italian",
"sense": "both injective and surjective",
"word": "biiettivo"
},
{
"_dis1": "93 7",
"code": "it",
"lang": "Italian",
"sense": "both injective and surjective",
"word": "bigettivo"
},
{
"_dis1": "93 7",
"alt": "ぜんたんしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "zentanshano",
"sense": "both injective and surjective",
"word": "全単射の"
},
{
"_dis1": "93 7",
"code": "pt",
"lang": "Portuguese",
"sense": "both injective and surjective",
"word": "bijetivo"
},
{
"_dis1": "93 7",
"code": "ro",
"lang": "Romanian",
"sense": "both injective and surjective",
"word": "bijectiv"
},
{
"_dis1": "93 7",
"code": "es",
"lang": "Spanish",
"sense": "both injective and surjective",
"word": "biyectivo"
},
{
"_dis1": "93 7",
"code": "sv",
"lang": "Swedish",
"sense": "both injective and surjective",
"word": "bijektiv"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "2002, Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, ACM Press, page 774:",
"text": "Proving the conjecture is equivalent to constructing a PCP that reads 2 symbols and accepts iff these symbols satisfy a bijective constraint.",
"type": "quote"
}
],
"glosses": [
"Having a component that is (specified to be) a bijective map; that specifies a bijective map."
],
"id": "en-bijective-en-adj-w6tenWLb",
"links": [
[
"mathematics",
"mathematics"
]
],
"raw_glosses": [
"(mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map."
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "3 97",
"code": "fi",
"lang": "Finnish",
"sense": "having a bijective map",
"word": "bijektiivinen"
}
]
}
],
"sounds": [
{
"rhymes": "-ɛktɪv"
}
],
"wikipedia": [
"Bijection"
],
"word": "bijective"
}
{
"head_templates": [
{
"args": {
"1": "fr",
"2": "adjective form"
},
"expansion": "bijective",
"name": "head"
}
],
"lang": "French",
"lang_code": "fr",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "French entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 2 entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
}
],
"form_of": [
{
"word": "bijectif"
}
],
"glosses": [
"feminine singular of bijectif"
],
"id": "en-bijective-fr-adj-N2zjLC5G",
"links": [
[
"bijectif",
"bijectif#French"
]
],
"tags": [
"feminine",
"form-of",
"singular"
]
}
],
"sounds": [
{
"ipa": "/bi.ʒɛk.tiv/"
},
{
"homophone": "bijectives"
}
],
"word": "bijective"
}
{
"categories": [
"English adjectives",
"English entries with incorrect language header",
"English lemmas",
"English uncomparable adjectives",
"Entries with translation boxes",
"Pages with 2 entries",
"Pages with entries",
"Rhymes:English/ɛktɪv",
"Rhymes:English/ɛktɪv/3 syllables",
"Terms with Catalan translations",
"Terms with Czech translations",
"Terms with Danish translations",
"Terms with Dutch translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Hungarian translations",
"Terms with Irish translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Mandarin translations",
"Terms with Portuguese translations",
"Terms with Romanian translations",
"Terms with Spanish translations",
"Terms with Swedish translations"
],
"derived": [
{
"word": "bijective numeration"
},
{
"word": "bijectively"
},
{
"word": "nonbijective"
},
{
"word": "bijectivity"
}
],
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "bijective (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "bijection"
},
{
"word": "injective"
},
{
"word": "surjective"
},
{
"word": "reversible"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Mathematics"
],
"examples": [
{
"text": "1987, James S. Royer, A Connotational Theory of Program Structure, Springer, LNCS 273, page 15,\nThen, by a straightforward, computable, bijective numerical coding, this idealized FORTRAN determines an EN. (Note: In this FORTRAN example, we could have omitted restrictions on I/O and instead used a computable, bijective, numerical coding for inputs and outputs to get another EN determined by FORTRAN.)"
},
{
"text": "1993, Susan Montgomery, Hopf Algebras and Their Actions on Rings, American Mathematical Society, CBMS, Regional Conference Series in Mathematics, Number 83, page 124,\nRecent experience indicates that for infinite-dimensional Hopf algebras, the “right” definition of Galois is to require that β be bijective."
},
{
"text": "2008, B. Aslan, M. T. Sakalli, E. Bulus, Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings, Joachim von zur Gathen, José Luis Imana, Çetin Kaya Koç (editors), Arithmetic of Finite Fields: 2nd International Workshop, Springer, LNCS 5130, page 131,\nGenerally, there is a parallel relation between the maximum differential value and maximum LAT value for bijective S-boxes."
},
{
"ref": "2010, Kang Feng, Mengzhao Qin, Symplectic Geometric Algorithms for Hamiltonian Systems, Springer, page 39:",
"text": "An isomorphism is a bijective homomorphism.",
"type": "quote"
},
{
"text": "2012 [Introduction to Graph Theory, McGraw-Hill], Gary Chartrand, Ping Zhang, A First Course in Graph Theory, 2013, Dover, Revised and corrected republication, page 64,\nThe proof that isomorphism is an equivalence relation relies on three fundamental properties of bijective functions (functions that are one-to-one and onto): (1) every identity function is bijective, (2) the inverse of every bijective function is also bijective, (3) the composition of two bijective functions is bijective."
}
],
"glosses": [
"Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"function",
"function"
],
[
"codomain",
"codomain"
],
[
"domain",
"domain"
],
[
"one-to-one",
"one-to-one"
],
[
"injective",
"injective"
],
[
"surjective",
"surjective"
]
],
"raw_glosses": [
"(mathematics, of a function) Associating to each element of the codomain exactly one element of the domain; establishing a perfect (one-to-one) correspondence between the elements of the domain and the codomain; (formally) both injective and surjective."
],
"raw_tags": [
"of a function"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Mathematics"
],
"examples": [
{
"ref": "2002, Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, ACM Press, page 774:",
"text": "Proving the conjecture is equivalent to constructing a PCP that reads 2 symbols and accepts iff these symbols satisfy a bijective constraint.",
"type": "quote"
}
],
"glosses": [
"Having a component that is (specified to be) a bijective map; that specifies a bijective map."
],
"links": [
[
"mathematics",
"mathematics"
]
],
"raw_glosses": [
"(mathematics) Having a component that is (specified to be) a bijective map; that specifies a bijective map."
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"rhymes": "-ɛktɪv"
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "both injective and surjective",
"word": "bijectiu"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "yīyīyìngshède",
"sense": "both injective and surjective",
"word": "一一映射的"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shuāngshède",
"sense": "both injective and surjective",
"word": "双射的"
},
{
"code": "cs",
"lang": "Czech",
"sense": "both injective and surjective",
"word": "bijektivní"
},
{
"code": "da",
"lang": "Danish",
"sense": "both injective and surjective",
"word": "bijektiv"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "both injective and surjective",
"word": "bijectief"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "both injective and surjective",
"word": "bijektiivinen"
},
{
"code": "fr",
"lang": "French",
"sense": "both injective and surjective",
"word": "bijectif"
},
{
"code": "de",
"lang": "German",
"sense": "both injective and surjective",
"word": "bijektiv"
},
{
"code": "de",
"lang": "German",
"sense": "both injective and surjective",
"word": "eineindeutig"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "both injective and surjective",
"word": "bijektív"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "both injective and surjective",
"word": "kölcsönösen egyértelmű"
},
{
"code": "ga",
"lang": "Irish",
"sense": "both injective and surjective",
"word": "détheilgeach"
},
{
"code": "it",
"lang": "Italian",
"sense": "both injective and surjective",
"word": "biiettivo"
},
{
"code": "it",
"lang": "Italian",
"sense": "both injective and surjective",
"word": "bigettivo"
},
{
"alt": "ぜんたんしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "zentanshano",
"sense": "both injective and surjective",
"word": "全単射の"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "both injective and surjective",
"word": "bijetivo"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "both injective and surjective",
"word": "bijectiv"
},
{
"code": "es",
"lang": "Spanish",
"sense": "both injective and surjective",
"word": "biyectivo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "both injective and surjective",
"word": "bijektiv"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "having a bijective map",
"word": "bijektiivinen"
}
],
"wikipedia": [
"Bijection"
],
"word": "bijective"
}
{
"head_templates": [
{
"args": {
"1": "fr",
"2": "adjective form"
},
"expansion": "bijective",
"name": "head"
}
],
"lang": "French",
"lang_code": "fr",
"pos": "adj",
"senses": [
{
"categories": [
"French 3-syllable words",
"French adjective forms",
"French entries with incorrect language header",
"French non-lemma forms",
"French terms with IPA pronunciation",
"French terms with homophones",
"Pages with 2 entries",
"Pages with entries"
],
"form_of": [
{
"word": "bijectif"
}
],
"glosses": [
"feminine singular of bijectif"
],
"links": [
[
"bijectif",
"bijectif#French"
]
],
"tags": [
"feminine",
"form-of",
"singular"
]
}
],
"sounds": [
{
"ipa": "/bi.ʒɛk.tiv/"
},
{
"homophone": "bijectives"
}
],
"word": "bijective"
}
Download raw JSONL data for bijective meaning in All languages combined (7.6kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-28 from the enwiktionary dump dated 2024-11-21 using wiktextract (65a6e81 and 0dbea76). 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.