"smooth function" meaning in All languages combined

See smooth function on Wiktionary

Noun [English]

Forms: smooth functions [plural]
Etymology: smooth + function Head templates: {{en-noun}} smooth function (plural smooth functions)
  1. (mathematics) a function that has derivatives of all finite orders everywhere in its domain. Wikipedia link: smooth function Categories (topical): Functions, Mathematics, Shapes Translations (function that has derivatives of all finite orders everywhere in its domain): slät funktion [common-gender] (Swedish), glatt funktion [common-gender] (Swedish)

Inflected forms

{
  "etymology_text": "smooth + function",
  "forms": [
    {
      "form": "smooth functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth function (plural smooth functions)",
      "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"
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          "source": "w"
        },
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        },
        {
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Functions",
          "orig": "en:Functions",
          "parents": [
            "Algebra",
            "Calculus",
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
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            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Shapes",
          "orig": "en:Shapes",
          "parents": [
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            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, →ISBN, page 419:",
          "text": "Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.",
          "type": "quote"
        }
      ],
      "glosses": [
        "a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "id": "en-smooth_function-en-noun-IipSbcIp",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "order",
          "order"
        ],
        [
          "domain",
          "domain"
        ]
      ],
      "raw_glosses": [
        "(mathematics) a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "function that has derivatives of all finite orders everywhere in its domain",
          "tags": [
            "common-gender"
          ],
          "word": "slät funktion"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "function that has derivatives of all finite orders everywhere in its domain",
          "tags": [
            "common-gender"
          ],
          "word": "glatt funktion"
        }
      ],
      "wikipedia": [
        "smooth function"
      ]
    }
  ],
  "word": "smooth function"
}
{
  "etymology_text": "smooth + function",
  "forms": [
    {
      "form": "smooth functions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "smooth function (plural smooth functions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        {
          "ref": "2003, Eric W. Weisstein, CRC Concise Encyclopedia of Mathematics, →ISBN, page 419:",
          "text": "Any ANALYTIC FUNCTION is smooth. But a smooth function is not necessarily analytic.",
          "type": "quote"
        }
      ],
      "glosses": [
        "a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "derivative",
          "derivative"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "order",
          "order"
        ],
        [
          "domain",
          "domain"
        ]
      ],
      "raw_glosses": [
        "(mathematics) a function that has derivatives of all finite orders everywhere in its domain."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "smooth function"
      ]
    }
  ],
  "translations": [
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function that has derivatives of all finite orders everywhere in its domain",
      "tags": [
        "common-gender"
      ],
      "word": "slät funktion"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "function that has derivatives of all finite orders everywhere in its domain",
      "tags": [
        "common-gender"
      ],
      "word": "glatt funktion"
    }
  ],
  "word": "smooth function"
}

Download raw JSONL data for smooth function meaning in All languages combined (1.6kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.