"partial function" meaning in English

{
  "antonyms": [
    {
      "english": "function whose domain is a subset of the set on which it is formally defined",
      "sense": "antonym(s) of",
      "topics": [
        "mathematics",
        "sciences"
      ],
      "word": "total function"
    }
  ],
  "forms": [
    {
      "form": "partial functions",
      "tags": [
        "plural"
      ]
    }
  ],
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    {
      "args": {},
      "expansion": "partial function (plural partial functions)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Functions",
          "orig": "en:Functions",
          "parents": [
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            "Calculus",
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1967 [John Wiley & Sons], Stephen Cole Kleene, Mathematical Logic, 2002, Dover, page 244,\nThe Church-Turing thesis applies to partial functions on the same grounds as to total functions (§ 41)."
        },
        {
          "text": "1991, Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella (editors), Algebraic System Specification and Development: A Survey and Annotated Bibliography, Springer, LNCS 501, page 15,\nNowadays it seems quite clear that if algebraic specifications are to be used as a powerful and realistic tool for the development of complex systems they should permit the specification of partial functions. […] There are essentially two ways of specifying partial functions."
        },
        {
          "text": "2006, Paulo Oliva, Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, John V. Tucker (editors), Logical Approaches to Computational Barriers: 2nd Conference on Computability in Europe, Proceedings, Springer, LNCS 3988, page 432,\nIn the following σ and τ will denote finite partial functions from N to N , i.e. partial functions which are defined on a finite domain. A partial function which is everywhere undefined is denoted by ⟨⟩, whereas a partial function defined only at position k (with value n) is denoted by ⟨k,n⟩."
        }
      ],
      "glosses": [
        "A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X."
      ],
      "id": "en-partial_function-en-noun-04~uhkpI",
      "links": [
        [
          "mathematics",
          "mathematics"
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        [
          "function",
          "function"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "subset",
          "subset"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "mathematics: a function whose domain is a subset of the set on which it is formally defined",
          "tags": [
            "neuter"
          ],
          "word": "hlutskilgreint fall"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "mathematics: a function whose domain is a subset of the set on which it is formally defined",
          "tags": [
            "feminine"
          ],
          "word": "funzione parziale"
        }
      ],
      "wikipedia": [
        "partial function"
      ]
    }
  ],
  "word": "partial function"
}

{
  "antonyms": [
    {
      "english": "function whose domain is a subset of the set on which it is formally defined",
      "sense": "antonym(s) of",
      "topics": [
        "mathematics",
        "sciences"
      ],
      "word": "total function"
    }
  ],
  "forms": [
    {
      "form": "partial functions",
      "tags": [
        "plural"
      ]
    }
  ],
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  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English entries with incorrect language header",
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        "English nouns",
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        "en:Functions",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "1967 [John Wiley & Sons], Stephen Cole Kleene, Mathematical Logic, 2002, Dover, page 244,\nThe Church-Turing thesis applies to partial functions on the same grounds as to total functions (§ 41)."
        },
        {
          "text": "1991, Michel Bidoit, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, Donald Sannella (editors), Algebraic System Specification and Development: A Survey and Annotated Bibliography, Springer, LNCS 501, page 15,\nNowadays it seems quite clear that if algebraic specifications are to be used as a powerful and realistic tool for the development of complex systems they should permit the specification of partial functions. […] There are essentially two ways of specifying partial functions."
        },
        {
          "text": "2006, Paulo Oliva, Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis, Arnold Beckmann, Ulrich Berger, Benedikt Löwe, John V. Tucker (editors), Logical Approaches to Computational Barriers: 2nd Conference on Computability in Europe, Proceedings, Springer, LNCS 3988, page 432,\nIn the following σ and τ will denote finite partial functions from N to N , i.e. partial functions which are defined on a finite domain. A partial function which is everywhere undefined is denoted by ⟨⟩, whereas a partial function defined only at position k (with value n) is denoted by ⟨k,n⟩."
        }
      ],
      "glosses": [
        "A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X."
      ],
      "links": [
        [
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        ],
        [
          "function",
          "function"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "subset",
          "subset"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A function whose domain is a subset of the set on which it is formally defined; i.e., a function f: X→Y for which values f(x) are defined only for x ∈ W, where W ⊆ X."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "partial function"
      ]
    }
  ],
  "translations": [
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "mathematics: a function whose domain is a subset of the set on which it is formally defined",
      "tags": [
        "neuter"
      ],
      "word": "hlutskilgreint fall"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "mathematics: a function whose domain is a subset of the set on which it is formally defined",
      "tags": [
        "feminine"
      ],
      "word": "funzione parziale"
    }
  ],
  "word": "partial function"
}