"transitive set" meaning in All languages combined

See transitive set on Wiktionary

Noun [English]

Forms: transitive sets [plural]
Head templates: {{en-noun}} transitive set (plural transitive sets)
  1. (set theory) Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X. Wikipedia link: transitive set Categories (topical): Set theory Derived forms: transitive closure
    Sense id: en-transitive_set-en-noun-p9N5qL5T Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: mathematics, sciences, set-theory

Inflected forms

{
  "forms": [
    {
      "form": "transitive sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "transitive set (plural transitive sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "transitive closure"
        }
      ],
      "glosses": [
        "Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X."
      ],
      "id": "en-transitive_set-en-noun-p9N5qL5T",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "urelement",
          "urelement"
        ]
      ],
      "raw_glosses": [
        "(set theory) Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "transitive set"
      ]
    }
  ],
  "word": "transitive set"
}
{
  "derived": [
    {
      "word": "transitive closure"
    }
  ],
  "forms": [
    {
      "form": "transitive sets",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "transitive set (plural transitive sets)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Set theory"
      ],
      "glosses": [
        "Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "urelement",
          "urelement"
        ]
      ],
      "raw_glosses": [
        "(set theory) Any set X such that for any x ∈ X, if y ∈ x then y ∈ X; equivalently, such that if x ∈ X and x is not an urelement then x ⊆ X."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "transitive set"
      ]
    }
  ],
  "word": "transitive set"
}

Download raw JSONL data for transitive set meaning in All languages combined (1.0kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.