"Zorn's lemma" meaning in English

See Zorn's lemma in All languages combined, or Wiktionary

Proper name

Etymology: After Max August Zorn 1906-1993, German-born American mathematician. See German Zorn. Etymology templates: {{m|de|Zorn}} Zorn Head templates: {{en-proper noun}} Zorn's lemma
  1. (set theory) A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element. Wikipedia link: Max August Zorn, Zorn's lemma Categories (topical): Set theory

Download JSON data for Zorn's lemma meaning in English (1.9kB)

{
  "etymology_templates": [
    {
      "args": {
        "1": "de",
        "2": "Zorn"
      },
      "expansion": "Zorn",
      "name": "m"
    }
  ],
  "etymology_text": "After Max August Zorn 1906-1993, German-born American mathematician. See German Zorn.",
  "head_templates": [
    {
      "args": {},
      "expansion": "Zorn's lemma",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element."
      ],
      "id": "en-Zorn's_lemma-en-name-lcOjQ3N1",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "proposition",
          "proposition"
        ],
        [
          "partially ordered",
          "partially ordered"
        ],
        [
          "chain",
          "chain"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "maximal",
          "maximal"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(set theory) A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "Max August Zorn",
        "Zorn's lemma"
      ]
    }
  ],
  "word": "Zorn's lemma"
}
{
  "etymology_templates": [
    {
      "args": {
        "1": "de",
        "2": "Zorn"
      },
      "expansion": "Zorn",
      "name": "m"
    }
  ],
  "etymology_text": "After Max August Zorn 1906-1993, German-born American mathematician. See German Zorn.",
  "head_templates": [
    {
      "args": {},
      "expansion": "Zorn's lemma",
      "name": "en-proper noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English uncountable nouns",
        "en:Set theory"
      ],
      "glosses": [
        "A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "proposition",
          "proposition"
        ],
        [
          "partially ordered",
          "partially ordered"
        ],
        [
          "chain",
          "chain"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "maximal",
          "maximal"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(set theory) A proposition of set theory stating that every partially ordered set, in which every chain (i.e. totally ordered subset) has an upper bound, contains at least one maximal element."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "Max August Zorn",
        "Zorn's lemma"
      ]
    }
  ],
  "word": "Zorn's lemma"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-20 from the enwiktionary dump dated 2024-05-02 using wiktextract (1d5a7d1 and 304864d). 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.