"cofinality" meaning in English

See cofinality in All languages combined, or Wiktionary

Noun

Forms: cofinalities [plural]
Etymology: Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-der. English co- English final English cofinal Proto-Indo-European *-teh₂ Proto-Indo-European *-ts Proto-Indo-European *-teh₂ts Latin -itāsder. Old French -itebor. Middle English -ite English -ity English cofinality From cofinal + -ity. Etymology templates: {{ety|en|:af|cofinal|-ity|text=+|tree=1}} Etymology tree Proto-Indo-European *ḱe? Proto-Indo-European *ḱóm Proto-Italic *kom Proto-Italic *kom- Latin con- Latin co-der. English co- English final English cofinal Proto-Indo-European *-teh₂ Proto-Indo-European *-ts Proto-Indo-European *-teh₂ts Latin -itāsder. Old French -itebor. Middle English -ite English -ity English cofinality [Appendix:Glossary#derived_terms|Derived]] from", "terms" : [ { "children" : [ { "terms" : [ { "id" : "bringing together", "children" : [ { "terms" : [ { "id" : "with", "children" : [ { "terms" : [ { "id" : "with", "children" : [ { "terms" : [ { "id" : "beside", "children" : [ { "terms" : [ { "is_uncertain" : true, "id" : "here", "children" : [ ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*ḱe", "lang" : "ine-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*ḱóm", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*kom", "lang" : "itc-pro" } ], "keyword_label" : "From", "keyword" : "from" } ], "status" : "ok", "lang_name" : "Proto-Italic", "term" : "*kom-", "lang" : "itc-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "status" : "ok", "lang_name" : "Latin", "term" : "con-", "lang" : "la" } ], "keyword_label" : "From", "keyword" : "from" } ], "lang_name" : "Latin", "term" : "co-", "status" : "ok", "lang" : "la" } ], "keyword" : "derived" } ], "lang_name" : "English", "term" : "co-", "status" : "ok", "lang" : "en" }, { "children" : [ ], "lang_name" : "English", "term" : "final", "status" : "missing", "lang" : "en" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "English", "term" : "cofinal", "status" : "ok", "lang" : "en" }, { "children" : [ { "terms" : [ { "children" : [ { "keyword_abbrev" : "bor.", "keyword_label" : "Borrowed from", "terms" : [ { "children" : [ { "keyword_abbrev" : "der.", "keyword_label" : "Derived from", "terms" : [ { "children" : [ { "terms" : [ { "id" : "-ty", "children" : [ { "terms" : [ { "children" : [ ], "lang_name" : "Proto-Indo-European", "term" : "*-teh₂", "status" : "ok", "lang" : "ine-pro" }, { "children" : [ ], "lang_name" : "Proto-Indo-European", "term" : "*-ts", "status" : "missing", "lang" : "ine-pro" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "status" : "ok", "lang_name" : "Proto-Indo-European", "term" : "*-teh₂ts", "lang" : "ine-pro" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "Latin", "term" : "-itās", "status" : "ok", "lang" : "la" } ], "keyword" : "derived" } ], "lang_name" : "Old French", "term" : "-ite", "status" : "inline", "lang" : "fro" } ], "keyword" : "bor" } ], "lang_name" : "Middle English", "term" : "-ite", "status" : "ok", "lang" : "enm" } ], "keyword_label" : "Inherited from", "keyword" : "inherited" } ], "lang_name" : "English", "term" : "-ity", "status" : "ok", "lang" : "en" } ], "keyword_label" : "From", "is_group" : true, "keyword" : "affix" } ], "lang_name" : "English", "term" : "cofinality", "status" : "ok", "lang" : "en" }" data-lang="en" data-title="cofinality"> From cofinal + -ity. Head templates: {{en-noun|~}} cofinality (countable and uncountable, plural cofinalities)
  1. (mathematics, countable) The least cardinality of a cofinal subset of a partially ordered set. Tags: countable Translations (the least of cardinalities of cofinal subsets): cofinalidad [feminine] (Spanish)
    Sense id: en-cofinality-en-noun-LDrTZlnO Categories (other): Mathematics, English entries referencing pages with etymology sections missing etymons, English entries with etymology texts, English entries with etymology trees, English entries with etymon, English entries with incorrect language header, English terms suffixed with -ity, Entries with translation boxes, Pages using etymon with no ID, Pages with 1 entry, Pages with entries, Pages with etymology trees, Pages with etymon, Terms with Polish translations, Terms with Spanish translations Disambiguation of English entries referencing pages with etymology sections missing etymons: 46 54 Disambiguation of English entries with etymology texts: 48 52 Disambiguation of English entries with etymology trees: 48 52 Disambiguation of English entries with etymon: 47 53 Disambiguation of English entries with incorrect language header: 58 42 Disambiguation of English terms suffixed with -ity: 54 46 Disambiguation of Entries with translation boxes: 58 42 Disambiguation of Pages using etymon with no ID: 54 46 Disambiguation of Pages with 1 entry: 57 43 Disambiguation of Pages with entries: 58 42 Disambiguation of Pages with etymology trees: 50 50 Disambiguation of Pages with etymon: 49 51 Disambiguation of Terms with Polish translations: 58 42 Disambiguation of Terms with Spanish translations: 61 39 Topics: mathematics, sciences Disambiguation of 'the least of cardinalities of cofinal subsets': 69 31
  2. (mathematics, uncountable) The property of being cofinal. Tags: uncountable Translations (the property of being cofinal): współkońcowość [feminine] (Polish)
    Sense id: en-cofinality-en-noun-3IkEGltR Categories (other): Mathematics, English entries referencing pages with etymology sections missing etymons, English entries with etymology texts, English entries with etymology trees, English entries with etymon, English terms suffixed with -ity, Pages using etymon with no ID, Pages with etymology trees, Pages with etymon Disambiguation of English entries referencing pages with etymology sections missing etymons: 46 54 Disambiguation of English entries with etymology texts: 48 52 Disambiguation of English entries with etymology trees: 48 52 Disambiguation of English entries with etymon: 47 53 Disambiguation of English terms suffixed with -ity: 54 46 Disambiguation of Pages using etymon with no ID: 54 46 Disambiguation of Pages with etymology trees: 50 50 Disambiguation of Pages with etymon: 49 51 Topics: mathematics, sciences Disambiguation of 'the property of being cofinal': 12 88
The following are not (yet) sense-disambiguated
Related terms: cofinal, coinitial, coinitiality

Inflected forms

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      "expansion": "Etymology tree\nProto-Indo-European *ḱe?\nProto-Indo-European *ḱóm\nProto-Italic *kom\nProto-Italic *kom-\nLatin con-\nLatin co-der.\nEnglish co-\nEnglish final\nEnglish cofinal\nProto-Indo-European *-teh₂\nProto-Indo-European *-ts\nProto-Indo-European *-teh₂ts\nLatin -itāsder.\nOld French -itebor.\nMiddle English -ite\nEnglish -ity\nEnglish cofinality\n[Appendix:Glossary#derived_terms|Derived]] from\", \"terms\" : [ { \"children\" : [ { \"terms\" : [ { \"id\" : \"bringing together\", \"children\" : [ { \"terms\" : [ { \"id\" : \"with\", \"children\" : [ { \"terms\" : [ { \"id\" : \"with\", \"children\" : [ { \"terms\" : [ { \"id\" : \"beside\", \"children\" : [ { \"terms\" : [ { \"is_uncertain\" : true, \"id\" : \"here\", \"children\" : [ ], \"status\" : \"ok\", \"lang_name\" : \"Proto-Indo-European\", \"term\" : \"*ḱe\", \"lang\" : \"ine-pro\" } ], \"keyword_label\" : \"From\", \"keyword\" : \"from\" } ], \"status\" : \"ok\", \"lang_name\" : \"Proto-Indo-European\", \"term\" : \"*ḱóm\", \"lang\" : \"ine-pro\" } ], \"keyword_label\" : \"Inherited from\", \"keyword\" : \"inherited\" } ], \"status\" : \"ok\", \"lang_name\" : \"Proto-Italic\", \"term\" : \"*kom\", \"lang\" : \"itc-pro\" } ], \"keyword_label\" : \"From\", \"keyword\" : \"from\" } ], \"status\" : \"ok\", \"lang_name\" : \"Proto-Italic\", \"term\" : \"*kom-\", \"lang\" : \"itc-pro\" } ], \"keyword_label\" : \"Inherited from\", \"keyword\" : \"inherited\" } ], \"status\" : \"ok\", \"lang_name\" : \"Latin\", \"term\" : \"con-\", \"lang\" : \"la\" } ], \"keyword_label\" : \"From\", \"keyword\" : \"from\" } ], \"lang_name\" : \"Latin\", \"term\" : \"co-\", \"status\" : \"ok\", \"lang\" : \"la\" } ], \"keyword\" : \"derived\" } ], \"lang_name\" : \"English\", \"term\" : \"co-\", \"status\" : \"ok\", \"lang\" : \"en\" }, { \"children\" : [ ], \"lang_name\" : \"English\", \"term\" : \"final\", \"status\" : \"missing\", \"lang\" : \"en\" } ], \"keyword_label\" : \"From\", \"is_group\" : true, \"keyword\" : \"affix\" } ], \"lang_name\" : \"English\", \"term\" : \"cofinal\", \"status\" : \"ok\", \"lang\" : \"en\" }, { \"children\" : [ { \"terms\" : [ { \"children\" : [ { \"keyword_abbrev\" : \"bor.\", \"keyword_label\" : \"Borrowed from\", \"terms\" : [ { \"children\" : [ { \"keyword_abbrev\" : \"der.\", \"keyword_label\" : \"Derived from\", \"terms\" : [ { \"children\" : [ { \"terms\" : [ { \"id\" : \"-ty\", \"children\" : [ { \"terms\" : [ { \"children\" : [ ], \"lang_name\" : \"Proto-Indo-European\", \"term\" : \"*-teh₂\", \"status\" : \"ok\", \"lang\" : \"ine-pro\" }, { \"children\" : [ ], \"lang_name\" : \"Proto-Indo-European\", \"term\" : \"*-ts\", \"status\" : \"missing\", \"lang\" : \"ine-pro\" } ], \"keyword_label\" : \"From\", \"is_group\" : true, \"keyword\" : \"affix\" } ], \"status\" : \"ok\", \"lang_name\" : \"Proto-Indo-European\", \"term\" : \"*-teh₂ts\", \"lang\" : \"ine-pro\" } ], \"keyword_label\" : \"Inherited from\", \"keyword\" : \"inherited\" } ], \"lang_name\" : \"Latin\", \"term\" : \"-itās\", \"status\" : \"ok\", \"lang\" : \"la\" } ], \"keyword\" : \"derived\" } ], \"lang_name\" : \"Old French\", \"term\" : \"-ite\", \"status\" : \"inline\", \"lang\" : \"fro\" } ], \"keyword\" : \"bor\" } ], \"lang_name\" : \"Middle English\", \"term\" : \"-ite\", \"status\" : \"ok\", \"lang\" : \"enm\" } ], \"keyword_label\" : \"Inherited from\", \"keyword\" : \"inherited\" } ], \"lang_name\" : \"English\", \"term\" : \"-ity\", \"status\" : \"ok\", \"lang\" : \"en\" } ], \"keyword_label\" : \"From\", \"is_group\" : true, \"keyword\" : \"affix\" } ], \"lang_name\" : \"English\", \"term\" : \"cofinality\", \"status\" : \"ok\", \"lang\" : \"en\" }\" data-lang=\"en\" data-title=\"cofinality\">\nFrom cofinal + -ity.",
      "name": "ety"
    }
  ],
  "etymology_text": "Etymology tree\nProto-Indo-European *ḱe?\nProto-Indo-European *ḱóm\nProto-Italic *kom\nProto-Italic *kom-\nLatin con-\nLatin co-der.\nEnglish co-\nEnglish final\nEnglish cofinal\nProto-Indo-European *-teh₂\nProto-Indo-European *-ts\nProto-Indo-European *-teh₂ts\nLatin -itāsder.\nOld French -itebor.\nMiddle English -ite\nEnglish -ity\nEnglish cofinality\nFrom cofinal + -ity.",
  "forms": [
    {
      "form": "cofinalities",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "cofinality (countable and uncountable, plural cofinalities)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "cofinal"
    },
    {
      "word": "coinitial"
    },
    {
      "word": "coinitiality"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English terms with quotations",
        "English terms with usage examples",
        "en:Mathematics"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              4,
              14
            ]
          ],
          "text": "The cofinality of any set with a greatest element is 1.",
          "type": "example"
        },
        {
          "bold_text_offsets": [
            [
              19,
              29
            ],
            [
              240,
              250
            ]
          ],
          "ref": "2024 November 12, Steffen Lempp, Alberto Marcone, Manlio Valenti, “Chains and antichains in the Weihrauch lattice”, in arXiv, page 1, archived from the original on 23 Jun 2026:",
          "text": "The dual notion of cofinality is coinitiality: a set S#92;subseteqP is called coinitial if for every p#92;inP there is q#92;inS such that q#92;lep. Equivalently, a coinitial set in P is a cofinal set in P#92;ast#58;#61;(P,#92;ge). […] Both cofinality and coinitiality need not be well-defined for an arbitrary partial order (e.g. if the partial order is only made of two incomparable elements).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The least cardinality of a cofinal subset of a partially ordered set."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "cardinality",
          "cardinality"
        ],
        [
          "cofinal",
          "cofinal"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ]
      ],
      "raw_glosses": [
        "(mathematics, countable) The least cardinality of a cofinal subset of a partially ordered set."
      ],
      "tags": [
        "countable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English uncountable nouns",
        "en:Mathematics"
      ],
      "glosses": [
        "The property of being cofinal."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "cofinal",
          "cofinal#English"
        ]
      ],
      "raw_glosses": [
        "(mathematics, uncountable) The property of being cofinal."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "es",
      "lang": "Spanish",
      "lang_code": "es",
      "sense": "the least of cardinalities of cofinal subsets",
      "tags": [
        "feminine"
      ],
      "word": "cofinalidad"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "lang_code": "pl",
      "sense": "the property of being cofinal",
      "tags": [
        "feminine"
      ],
      "word": "współkońcowość"
    }
  ],
  "word": "cofinality"
}

Download raw JSONL data for cofinality meaning in English (7.3kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2026-07-25 from the enwiktionary dump dated 2026-07-06 using wiktextract (d9fa233 and 9e92f4b). 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.