"transitive closure" meaning in All languages combined

See transitive closure on Wiktionary

Noun [English]

Forms: transitive closures [plural]
Head templates: {{en-noun}} transitive closure (plural transitive closures)
  1. (set theory, order theory, of a binary relation R on a set X) The smallest binary relation on X that includes R and is transitive.
    Sense id: en-transitive_closure-en-noun-0c2cFl1i Categories (other): Set theory Topics: mathematics, order-theory, sciences, set-theory
  2. (set theory, of a set X) The smallest transitive set that contains X.
    Sense id: en-transitive_closure-en-noun-iv4DPLXT Categories (other): Set theory, English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 10 90 Disambiguation of Pages with 1 entry: 5 95 Disambiguation of Pages with entries: 4 96 Topics: mathematics, sciences, set-theory

Inflected forms

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      "raw_glosses": [
        "(set theory, order theory, of a binary relation R on a set X) The smallest binary relation on X that includes R and is transitive."
      ],
      "raw_tags": [
        "of a binary relation R on a set X"
      ],
      "topics": [
        "mathematics",
        "order-theory",
        "sciences",
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          "parents": [],
          "source": "w+disamb"
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        "(set theory, of a set X) The smallest transitive set that contains X."
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    "English nouns",
    "Pages with 1 entry",
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  ],
  "forms": [
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      "tags": [
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      ],
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        "The smallest transitive set that contains X."
      ],
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          "set theory",
          "set theory"
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        ]
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        "(set theory, of a set X) The smallest transitive set that contains X."
      ],
      "raw_tags": [
        "of a set X"
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        "mathematics",
        "sciences",
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    "Transitive set#Transitive closure"
  ],
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}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-27 from the enwiktionary dump dated 2025-05-20 using wiktextract (a4e883e and f1c2b61). 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.