"binary relation" meaning in English

See binary relation in All languages combined, or Wiktionary

Noun

Forms: binary relations [plural]
Head templates: {{en-noun}} binary relation (plural binary relations)
  1. (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). Categories (topical): Set theory
    Sense id: en-binary_relation-en-noun-QVsM9Asj Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Czech translations, Terms with Finnish translations, Terms with French translations, Terms with Hungarian translations, Terms with Icelandic translations, Terms with Italian translations, Terms with Japanese translations, Terms with Romanian translations, Terms with Spanish translations Disambiguation of English entries with incorrect language header: 61 39 Disambiguation of Entries with translation boxes: 63 37 Disambiguation of Pages with 1 entry: 62 38 Disambiguation of Pages with entries: 64 36 Disambiguation of Terms with Czech translations: 61 39 Disambiguation of Terms with Finnish translations: 65 35 Disambiguation of Terms with French translations: 65 35 Disambiguation of Terms with Hungarian translations: 57 43 Disambiguation of Terms with Icelandic translations: 65 35 Disambiguation of Terms with Italian translations: 66 34 Disambiguation of Terms with Japanese translations: 66 34 Disambiguation of Terms with Romanian translations: 65 35 Disambiguation of Terms with Spanish translations: 66 34 Topics: mathematics, order-theory, sciences, set-theory
  2. (set theory, order theory, "on" or "between" sets A and B) A subset of the Cartesian product A×B. Categories (topical): Set theory
    Sense id: en-binary_relation-en-noun-L9v2tqxj Topics: mathematics, order-theory, sciences, set-theory
The following are not (yet) sense-disambiguated
Synonyms: correspondence [order-theory, mathematics, sciences], dyadic relation [order-theory, mathematics, sciences], 2-place relation [order-theory, mathematics, sciences] Hyponyms: dependency relation [order-theory, mathematics, sciences], equivalence relation [order-theory, mathematics, sciences] Related terms: nil relation (english: the empty set), universal relation (alt: the entire set A×A) Translations (order theory): binární relace [feminine] (Czech), binäärirelaatio (Finnish), relation binaire [feminine] (French), kétváltozós reláció (Hungarian), tvístæð vensl [neuter, plural] (Icelandic), relazione binaria [feminine] (Italian), 二項関係 (nikō-kankei) (Japanese), relație binară [feminine] (Romanian), relación binaria [feminine] (Spanish)
Disambiguation of 'order theory': 50 50

Inflected forms

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      "_dis1": "0 0",
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      "word": "dependency relation"
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      "_dis1": "0 0",
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      "word": "equivalence relation"
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "_dis1": "0 0",
      "english": "the empty set",
      "word": "nil relation"
    },
    {
      "_dis1": "0 0",
      "alt": "the entire set A×A",
      "word": "universal relation"
    }
  ],
  "senses": [
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          "_dis": "66 34",
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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": "quote"
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        {
          "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": "quote"
        },
        {
          "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": "quote"
        }
      ],
      "glosses": [
        "A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A)."
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        [
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      "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)."
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      "topics": [
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        "order-theory",
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      "qualifier": "\"on\" or \"between\" sets A and B",
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      "_dis1": "0 0",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
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      "word": "correspondence"
    },
    {
      "_dis1": "0 0",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
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      "word": "dyadic relation"
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    {
      "_dis1": "0 0",
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
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      "word": "2-place relation"
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      "_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"
    }
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  "wikipedia": [
    "binary relation"
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  "word": "binary relation"
}
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      "english": "the empty set",
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        "(set theory, order theory, \"on\" or \"between\" sets A and B) A subset of the Cartesian product A×B."
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      "topics": [
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      "word": "correspondence"
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      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "dyadic relation"
    },
    {
      "topics": [
        "order-theory",
        "mathematics",
        "sciences"
      ],
      "word": "2-place relation"
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  "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"
}

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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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