"epsilontic" meaning in All languages combined

{
  "etymology_text": "From the fact that ε is the usual symbol used to denote an error bound.",
  "head_templates": [
    {
      "args": {
        "1": "?"
      },
      "expansion": "epsilontic",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "epsilontics"
        }
      ],
      "examples": [
        {
          "ref": "1966, J. C. Oxtoby, B. J. Pettis, G. B. Price, John Von Neumann, 1903-1957, American Mathematical Soc., →ISBN, page 88:",
          "text": "The question is of a technical, gymnastic kind, and von Neumann's positive answer [4] uses the set-theoretic and epsilontic trickery appropriate to this domain.",
          "type": "quote"
        },
        {
          "ref": "1969, J. M. Ziman, Elements of Advanced Quantum Theory, Cambridge University Press, →ISBN, page 238:",
          "text": "If a parameter such as x in (7.71) is continuous, there are other operations of the group 'as close as one likes' to any given operation; in 'epsilontic' language, we must be able to write T(x + ε) → T(x) as ε → 0. (7.76)",
          "type": "quote"
        },
        {
          "ref": "1996, Ronald Calinger, Vita Mathematica: Historical Research and Integration with Teaching, Cambridge University Press, →ISBN, page 168:",
          "text": "Weierstrass precisely defines a function in the modern sense as a correspondence between two variable quantities—a definition he attributes to Fourier, Cauchy, and Dirichlet—and develops the epsilontic method.",
          "type": "quote"
        },
        {
          "ref": "2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 44:",
          "text": "Riemann definitely accepts the epsilontic justification of limit analysis, as shown by his well-known introduction of the concept of the integral in his habilitation paper of 1853 (W. 239), and, more fully, by this paper as a whole.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals."
      ],
      "id": "en-epsilontic-en-adj-SqTpg7IX",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "explicit",
          "explicit"
        ],
        [
          "error",
          "error"
        ],
        [
          "bound",
          "bound"
        ],
        [
          "estimation",
          "estimation"
        ],
        [
          "infinitesimal",
          "infinitesimal"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "epsilontic"
}

{
  "derived": [
    {
      "word": "epsilontics"
    }
  ],
  "etymology_text": "From the fact that ε is the usual symbol used to denote an error bound.",
  "head_templates": [
    {
      "args": {
        "1": "?"
      },
      "expansion": "epsilontic",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        "English adjectives",
        "English entries with incorrect language header",
        "English lemmas",
        "English terms with quotations",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1966, J. C. Oxtoby, B. J. Pettis, G. B. Price, John Von Neumann, 1903-1957, American Mathematical Soc., →ISBN, page 88:",
          "text": "The question is of a technical, gymnastic kind, and von Neumann's positive answer [4] uses the set-theoretic and epsilontic trickery appropriate to this domain.",
          "type": "quote"
        },
        {
          "ref": "1969, J. M. Ziman, Elements of Advanced Quantum Theory, Cambridge University Press, →ISBN, page 238:",
          "text": "If a parameter such as x in (7.71) is continuous, there are other operations of the group 'as close as one likes' to any given operation; in 'epsilontic' language, we must be able to write T(x + ε) → T(x) as ε → 0. (7.76)",
          "type": "quote"
        },
        {
          "ref": "1996, Ronald Calinger, Vita Mathematica: Historical Research and Integration with Teaching, Cambridge University Press, →ISBN, page 168:",
          "text": "Weierstrass precisely defines a function in the modern sense as a correspondence between two variable quantities—a definition he attributes to Fourier, Cauchy, and Dirichlet—and develops the epsilontic method.",
          "type": "quote"
        },
        {
          "ref": "2009, Detlef Laugwitz, Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics, Springer Science & Business Media, →ISBN, page 44:",
          "text": "Riemann definitely accepts the epsilontic justification of limit analysis, as shown by his well-known introduction of the concept of the integral in his habilitation paper of 1853 (W. 239), and, more fully, by this paper as a whole.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "explicit",
          "explicit"
        ],
        [
          "error",
          "error"
        ],
        [
          "bound",
          "bound"
        ],
        [
          "estimation",
          "estimation"
        ],
        [
          "infinitesimal",
          "infinitesimal"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Pertaining to mathematical analysis using explicit error bound estimation and the epsilon-delta definition of a limit, especially as opposed to using infinitesimals."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "epsilontic"
}