See binary relation on Wiktionary
Download JSON data for binary relation meaning in All languages combined (4.7kB)
{
"forms": [
{
"form": "binary relations",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "binary relation (plural binary relations)",
"name": "en-noun"
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],
"hyponyms": [
{
"_dis1": "50 50",
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "dependency relation"
},
{
"_dis1": "50 50",
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "equivalence relation"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"_dis1": "50 50",
"english": "the empty set",
"word": "nil relation"
},
{
"_dis1": "50 50",
"alt": "the entire set A×A",
"word": "universal relation"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Set theory",
"orig": "en:Set theory",
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"Fundamental"
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"source": "w"
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{
"_dis": "61 39",
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{
"ref": "1978, George Grätzer, General Lattice Theory, Academic Press, page 1",
"text": "A partially ordered set #x5C;langleA,#x5C;varrho#x5C;rangle consists of a nonvoid set A and a binary relation #x5C;varrho on A, such that #x5C;varrho satisfies properties (P1)-(P3).",
"type": "quotation"
},
{
"ref": "1999, James C. Moore, Mathematical Methods for Economic Theory 1, Springer, page 24",
"text": "1.30. Corollary. If P is a binary relation which is asymmetric and negatively transitive, then P is also transitive.\nIt should be noted that a binary relation may be irreflexive and negatively transitive without being transitive; as an example, consider the standard inequality relation (≠).",
"type": "quotation"
},
{
"ref": "2005, T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer, page 1",
"text": "Definition If E is a non-empty set then by an order on E we mean a binary relation on E that is reflexive, anti-symmetric, and transitive.",
"type": "quotation"
}
],
"glosses": [
"A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A)."
],
"id": "en-binary_relation-en-noun-QVsM9Asj",
"links": [
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"set theory",
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"Cartesian product"
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"ordered pair",
"ordered pair"
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[
"element",
"element"
]
],
"qualifier": "\"on\" a set A",
"raw_glosses": [
"(set theory, order theory, \"on\" a set A) A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A)."
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
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{
"categories": [
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"kind": "topical",
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],
"glosses": [
"A subset of the Cartesian product A×B."
],
"id": "en-binary_relation-en-noun-L9v2tqxj",
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"qualifier": "\"on\" or \"between\" sets A and B",
"raw_glosses": [
"(set theory, order theory, \"on\" or \"between\" sets A and B) A subset of the Cartesian product A×B."
],
"topics": [
"mathematics",
"order-theory",
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}
],
"synonyms": [
{
"_dis1": "50 50",
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "correspondence"
},
{
"_dis1": "50 50",
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "dyadic relation"
},
{
"_dis1": "50 50",
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "2-place relation"
}
],
"translations": [
{
"_dis1": "50 50",
"code": "cs",
"lang": "Czech",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "binární relace"
},
{
"_dis1": "50 50",
"code": "fi",
"lang": "Finnish",
"sense": "order theory",
"word": "binäärirelaatio"
},
{
"_dis1": "50 50",
"code": "fr",
"lang": "French",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relation binaire"
},
{
"_dis1": "50 50",
"code": "hu",
"lang": "Hungarian",
"sense": "order theory",
"word": "kétváltozós reláció"
},
{
"_dis1": "50 50",
"code": "is",
"lang": "Icelandic",
"sense": "order theory",
"tags": [
"neuter",
"plural"
],
"word": "tvístæð vensl"
},
{
"_dis1": "50 50",
"code": "it",
"lang": "Italian",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relazione binaria"
},
{
"_dis1": "50 50",
"code": "ja",
"lang": "Japanese",
"roman": "nikō-kankei",
"sense": "order theory",
"word": "二項関係"
},
{
"_dis1": "50 50",
"code": "ro",
"lang": "Romanian",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relație binară"
},
{
"_dis1": "50 50",
"code": "es",
"lang": "Spanish",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relación binaria"
}
],
"wikipedia": [
"binary relation"
],
"word": "binary relation"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns"
],
"forms": [
{
"form": "binary relations",
"tags": [
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"topics": [
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"word": "dependency relation"
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{
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "equivalence relation"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"english": "the empty set",
"word": "nil relation"
},
{
"alt": "the entire set A×A",
"word": "universal relation"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Set theory"
],
"examples": [
{
"ref": "1978, George Grätzer, General Lattice Theory, Academic Press, page 1",
"text": "A partially ordered set #x5C;langleA,#x5C;varrho#x5C;rangle consists of a nonvoid set A and a binary relation #x5C;varrho on A, such that #x5C;varrho satisfies properties (P1)-(P3).",
"type": "quotation"
},
{
"ref": "1999, James C. Moore, Mathematical Methods for Economic Theory 1, Springer, page 24",
"text": "1.30. Corollary. If P is a binary relation which is asymmetric and negatively transitive, then P is also transitive.\nIt should be noted that a binary relation may be irreflexive and negatively transitive without being transitive; as an example, consider the standard inequality relation (≠).",
"type": "quotation"
},
{
"ref": "2005, T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer, page 1",
"text": "Definition If E is a non-empty set then by an order on E we mean a binary relation on E that is reflexive, anti-symmetric, and transitive.",
"type": "quotation"
}
],
"glosses": [
"A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A)."
],
"links": [
[
"set theory",
"set theory"
],
[
"subset",
"subset"
],
[
"Cartesian product",
"Cartesian product"
],
[
"ordered pair",
"ordered pair"
],
[
"element",
"element"
]
],
"qualifier": "\"on\" a set A",
"raw_glosses": [
"(set theory, order theory, \"on\" a set A) A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A)."
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
]
},
{
"categories": [
"en:Set theory"
],
"glosses": [
"A subset of the Cartesian product A×B."
],
"links": [
[
"set theory",
"set theory"
],
[
"subset",
"subset"
],
[
"Cartesian product",
"Cartesian product"
]
],
"qualifier": "\"on\" or \"between\" sets A and B",
"raw_glosses": [
"(set theory, order theory, \"on\" or \"between\" sets A and B) A subset of the Cartesian product A×B."
],
"topics": [
"mathematics",
"order-theory",
"sciences",
"set-theory"
]
}
],
"synonyms": [
{
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "correspondence"
},
{
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "dyadic relation"
},
{
"topics": [
"order-theory",
"mathematics",
"sciences"
],
"word": "2-place relation"
}
],
"translations": [
{
"code": "cs",
"lang": "Czech",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "binární relace"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "order theory",
"word": "binäärirelaatio"
},
{
"code": "fr",
"lang": "French",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relation binaire"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "order theory",
"word": "kétváltozós reláció"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "order theory",
"tags": [
"neuter",
"plural"
],
"word": "tvístæð vensl"
},
{
"code": "it",
"lang": "Italian",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relazione binaria"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "nikō-kankei",
"sense": "order theory",
"word": "二項関係"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relație binară"
},
{
"code": "es",
"lang": "Spanish",
"sense": "order theory",
"tags": [
"feminine"
],
"word": "relación binaria"
}
],
"wikipedia": [
"binary relation"
],
"word": "binary relation"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-04-26 from the enwiktionary dump dated 2024-04-21 using wiktextract (93a6c53 and 21a9316). 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.
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