"monotone convergence theorem" meaning in English

See monotone convergence theorem in All languages combined, or Wiktionary

Proper name

Head templates: {{en-prop}} monotone convergence theorem
  1. (mathematical analysis) A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent. Wikipedia link: monotone convergence theorem Categories (topical): Mathematical analysis Derived forms: MCT [abbreviation]
    Sense id: en-monotone_convergence_theorem-en-name-QIBzq4Y4 Categories (other): English entries with incorrect language header Topics: mathematical-analysis, mathematics, sciences

Alternative forms

Download JSON data for monotone convergence theorem meaning in English (1.4kB)

{
  "head_templates": [
    {
      "args": {},
      "expansion": "monotone convergence theorem",
      "name": "en-prop"
    }
  ],
  "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": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "tags": [
            "abbreviation"
          ],
          "word": "MCT"
        }
      ],
      "glosses": [
        "A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent."
      ],
      "id": "en-monotone_convergence_theorem-en-name-QIBzq4Y4",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "monotonic",
          "monotonic"
        ],
        [
          "increasing",
          "increasing"
        ],
        [
          "decreasing",
          "decreasing"
        ],
        [
          "bounded",
          "bounded"
        ],
        [
          "convergent",
          "convergent"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "monotone convergence theorem"
      ]
    }
  ],
  "word": "monotone convergence theorem"
}
{
  "derived": [
    {
      "tags": [
        "abbreviation"
      ],
      "word": "MCT"
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "monotone convergence theorem",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English uncountable nouns",
        "en:Mathematical analysis"
      ],
      "glosses": [
        "A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "monotonic",
          "monotonic"
        ],
        [
          "increasing",
          "increasing"
        ],
        [
          "decreasing",
          "decreasing"
        ],
        [
          "bounded",
          "bounded"
        ],
        [
          "convergent",
          "convergent"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A theorem which states that any sequence which is monotonic (either increasing or decreasing) and bounded is convergent."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "monotone convergence theorem"
      ]
    }
  ],
  "word": "monotone convergence theorem"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.