"dual number" meaning in English

See dual number in All languages combined, or Wiktionary

Noun

Forms: dual numbers [plural]
Head templates: {{en-noun}} dual number (plural dual numbers)
  1. (grammar) A grammatical number denoting a quantity of exactly two. Categories (topical): Grammar Related terms: nilpotent
    Sense id: en-dual_number-en-noun-FUL98GxH Topics: grammar, human-sciences, linguistics, sciences
  2. (algebra) An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0. Categories (topical): Algebra, Numbers Translations (element of the algebra of dual numbers): liczba dualna [feminine] (Polish)
    Sense id: en-dual_number-en-noun-hhaSfaEz Disambiguation of Numbers: 32 68 Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms with non-redundant non-automated sortkeys Disambiguation of English entries with incorrect language header: 31 69 Disambiguation of English entries with topic categories using raw markup: 34 66 Disambiguation of English terms with non-redundant non-automated sortkeys: 31 69 Topics: algebra, mathematics, sciences Disambiguation of 'element of the algebra of dual numbers': 12 88

Inflected forms

Download JSON data for dual number meaning in English (6.0kB)

{
  "forms": [
    {
      "form": "dual numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "dual number (plural dual numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Grammar",
          "orig": "en:Grammar",
          "parents": [
            "Linguistics",
            "Language",
            "Social sciences",
            "Communication",
            "Sciences",
            "Society",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1840, George Grey, A Vocabulary of the Dialects of South Western Australia, 2nd edition, T. & W. Boone, page xi",
          "text": "This is particularly the case with regard to the pronouns of the dual number, which form one of the peculiarities of the language.",
          "type": "quotation"
        },
        {
          "ref": "1998, William Blake Tyrrell, Larry J. Bennett, Recapturing Sophocles' Antigone, Rowman & Littlefield, page 43",
          "text": "Eteocles and Polyneices are enemy brothers, that is, they are alike in spite of the difference erected by being on opposite sides of the Theban battlements.¹ By uniting them with the dual number in the description of their deaths, Sophocles has the elders speak of them as indistinguishable in their hatred, spear work, and deaths.",
          "type": "quotation"
        },
        {
          "ref": "2006, Andrea Albrette, Teach Yourself Slovene, McGraw-Hill, page 19",
          "text": "In most languages, singular and plural are used to indicate number. Slovene, however, has an additional ‘dual’ number, which is used when referring to two of anything. This dual number existed in many languages at one stage in their development, but has been lost; in Slovene, though, […]",
          "type": "quotation"
        },
        {
          "ref": "2009, Giuliano Lancioni, “Formulaic models and formulaicity in Classical and Modern Standard Arabic”, in Roberta Corrigan, Edith A. Moravcsik, Hamid Ouali, Kathleen M. Wheatley, editors, Formulaic Language, Volume 1: Distribution and historical change, John Benjamins Publishing Company, page 225",
          "text": "Classical Arabic has a fully functional dual number, which requires dual agreement in verbs, adjectives and pronouns.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A grammatical number denoting a quantity of exactly two."
      ],
      "id": "en-dual_number-en-noun-FUL98GxH",
      "links": [
        [
          "grammar",
          "grammar"
        ],
        [
          "number",
          "number"
        ]
      ],
      "raw_glosses": [
        "(grammar) A grammatical number denoting a quantity of exactly two."
      ],
      "related": [
        {
          "_dis1": "61 39",
          "word": "nilpotent"
        }
      ],
      "topics": [
        "grammar",
        "human-sciences",
        "linguistics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "31 69",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "34 66",
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "31 69",
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "32 68",
          "kind": "topical",
          "langcode": "en",
          "name": "Numbers",
          "orig": "en:Numbers",
          "parents": [
            "All topics",
            "Terms by semantic function",
            "Fundamental"
          ],
          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "If f(x) is a polynomial or a power series then its derivative can be obtained “automatically” using dual numbers as follows: f'(x)#x3D;#x7B;f(x#x2B;#x5C;epsilon)-f(x)#x5C;over#x5C;epsilon#x7D; where f(x#x2B;#x5C;epsilon) should be expanded using the algebra of dual numbers. The role of the ε is therein similar to that of an infinitesimal.",
          "type": "example"
        },
        {
          "ref": "1993, Ivan Kolář, Peter W. Michor, Jan Slovák, Natural Operations in Differential Geometry, Springer, page 336",
          "text": "In the special case of the algebra #x5C;mathbf#x7B;D#x7D; of dual numbers we get the vertical tangent bundle V.",
          "type": "quotation"
        },
        {
          "ref": "1996, Andrei N. Kolmogorov, Adolf-Andrei P. Yushkevich, translated by Roger Cooke, Mathematics of the 19th Century: Geometry, Analytic Function Theory, Birkhäuser, page 87",
          "text": "These numbers are now called dual numbers (a term due to Study) and can be defined as expressions of the form a#x2B;b#x5C;epsilon, #x5C;epsilon²#x3D;0. When this is done as Kotel'nikov and Study showed, the dual distance between two points of this sphere representing two lines, forming an angle #x5C;varphi and having shortest distance d, is equal to the dual number #x5C;varphi#x2B;#x5C;epsilond, while the motions of Euclidean space are represented by rotations of the dual sphere, and consequently depend on three dual parameters.",
          "type": "quotation"
        },
        {
          "ref": "2002, Jiří Tomáš, “Some Classification Problems on Natural Bundles Related to Weil Bundles”, in Olga Gil-Medrano, Vicente Miquel, editors, Differential Geometry, Valencia 2001: Proceedings of the International Conference, World Scientific, page 297",
          "text": "Thus we investigate natural T-functions defined on T#x2A;T#x7B;#x5C;mathbf#x7B;D#x7D;#x5C;otimesA#x7D;M to determine all natural operators T#x5C;toTT#x2A;Tᴬ for #x5C;mathbf#x7B;D#x7D; denoting the algebra of dual numbers.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0."
      ],
      "id": "en-dual_number-en-noun-hhaSfaEz",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "real numbers",
          "real numbers"
        ]
      ],
      "raw_glosses": [
        "(algebra) An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "12 88",
          "code": "pl",
          "lang": "Polish",
          "sense": "element of the algebra of dual numbers",
          "tags": [
            "feminine"
          ],
          "word": "liczba dualna"
        }
      ]
    }
  ],
  "word": "dual number"
}
{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English entries with topic categories using raw markup",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "English terms with non-redundant non-automated sortkeys",
    "Requests for review of Welsh translations",
    "en:Numbers"
  ],
  "forms": [
    {
      "form": "dual numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "dual number (plural dual numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "nilpotent"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Grammar"
      ],
      "examples": [
        {
          "ref": "1840, George Grey, A Vocabulary of the Dialects of South Western Australia, 2nd edition, T. & W. Boone, page xi",
          "text": "This is particularly the case with regard to the pronouns of the dual number, which form one of the peculiarities of the language.",
          "type": "quotation"
        },
        {
          "ref": "1998, William Blake Tyrrell, Larry J. Bennett, Recapturing Sophocles' Antigone, Rowman & Littlefield, page 43",
          "text": "Eteocles and Polyneices are enemy brothers, that is, they are alike in spite of the difference erected by being on opposite sides of the Theban battlements.¹ By uniting them with the dual number in the description of their deaths, Sophocles has the elders speak of them as indistinguishable in their hatred, spear work, and deaths.",
          "type": "quotation"
        },
        {
          "ref": "2006, Andrea Albrette, Teach Yourself Slovene, McGraw-Hill, page 19",
          "text": "In most languages, singular and plural are used to indicate number. Slovene, however, has an additional ‘dual’ number, which is used when referring to two of anything. This dual number existed in many languages at one stage in their development, but has been lost; in Slovene, though, […]",
          "type": "quotation"
        },
        {
          "ref": "2009, Giuliano Lancioni, “Formulaic models and formulaicity in Classical and Modern Standard Arabic”, in Roberta Corrigan, Edith A. Moravcsik, Hamid Ouali, Kathleen M. Wheatley, editors, Formulaic Language, Volume 1: Distribution and historical change, John Benjamins Publishing Company, page 225",
          "text": "Classical Arabic has a fully functional dual number, which requires dual agreement in verbs, adjectives and pronouns.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A grammatical number denoting a quantity of exactly two."
      ],
      "links": [
        [
          "grammar",
          "grammar"
        ],
        [
          "number",
          "number"
        ]
      ],
      "raw_glosses": [
        "(grammar) A grammatical number denoting a quantity of exactly two."
      ],
      "topics": [
        "grammar",
        "human-sciences",
        "linguistics",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with quotations",
        "English terms with usage examples",
        "en:Algebra"
      ],
      "examples": [
        {
          "text": "If f(x) is a polynomial or a power series then its derivative can be obtained “automatically” using dual numbers as follows: f'(x)#x3D;#x7B;f(x#x2B;#x5C;epsilon)-f(x)#x5C;over#x5C;epsilon#x7D; where f(x#x2B;#x5C;epsilon) should be expanded using the algebra of dual numbers. The role of the ε is therein similar to that of an infinitesimal.",
          "type": "example"
        },
        {
          "ref": "1993, Ivan Kolář, Peter W. Michor, Jan Slovák, Natural Operations in Differential Geometry, Springer, page 336",
          "text": "In the special case of the algebra #x5C;mathbf#x7B;D#x7D; of dual numbers we get the vertical tangent bundle V.",
          "type": "quotation"
        },
        {
          "ref": "1996, Andrei N. Kolmogorov, Adolf-Andrei P. Yushkevich, translated by Roger Cooke, Mathematics of the 19th Century: Geometry, Analytic Function Theory, Birkhäuser, page 87",
          "text": "These numbers are now called dual numbers (a term due to Study) and can be defined as expressions of the form a#x2B;b#x5C;epsilon, #x5C;epsilon²#x3D;0. When this is done as Kotel'nikov and Study showed, the dual distance between two points of this sphere representing two lines, forming an angle #x5C;varphi and having shortest distance d, is equal to the dual number #x5C;varphi#x2B;#x5C;epsilond, while the motions of Euclidean space are represented by rotations of the dual sphere, and consequently depend on three dual parameters.",
          "type": "quotation"
        },
        {
          "ref": "2002, Jiří Tomáš, “Some Classification Problems on Natural Bundles Related to Weil Bundles”, in Olga Gil-Medrano, Vicente Miquel, editors, Differential Geometry, Valencia 2001: Proceedings of the International Conference, World Scientific, page 297",
          "text": "Thus we investigate natural T-functions defined on T#x2A;T#x7B;#x5C;mathbf#x7B;D#x7D;#x5C;otimesA#x7D;M to determine all natural operators T#x5C;toTT#x2A;Tᴬ for #x5C;mathbf#x7B;D#x7D; denoting the algebra of dual numbers.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "real numbers",
          "real numbers"
        ]
      ],
      "raw_glosses": [
        "(algebra) An element of an algebra (the algebra of dual numbers) which includes the real numbers and an element ε which satisfies ε ≠ 0 and ε² = 0."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "element of the algebra of dual numbers",
      "tags": [
        "feminine"
      ],
      "word": "liczba dualna"
    }
  ],
  "word": "dual number"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 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.