"nonstandard analysis" meaning in English

{
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      "expansion": "nonstandard analysis (uncountable)",
      "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",
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2010 February 25, Joel David Hamkins, “Answer to \"How helpful is non-standard analysis?\"”, in mathoverflow.net, retrieved 2012-11-13",
          "text": "To be sure, the epsilon-delta methods arose in part because mathematicians became unsure of the foundational validity of infinitesimals. But since nonstandard analysis exactly provides the missing legitimacy, the original motivation for adopting epsilon-delta arguments appears to fall away.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials."
      ],
      "id": "en-nonstandard_analysis-en-noun-6cMKjsWO",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "Analysis",
          "analysis"
        ],
        [
          "hyperreal number",
          "hyperreal number"
        ],
        [
          "infinitesimal",
          "infinitesimal"
        ],
        [
          "differential",
          "differential"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Nichtstandardanalysis"
        }
      ]
    }
  ],
  "word": "nonstandard analysis"
}

{
  "head_templates": [
    {
      "args": {
        "1": "-"
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      "expansion": "nonstandard analysis (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "Translation table header lacks gloss",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "ref": "2010 February 25, Joel David Hamkins, “Answer to \"How helpful is non-standard analysis?\"”, in mathoverflow.net, retrieved 2012-11-13",
          "text": "To be sure, the epsilon-delta methods arose in part because mathematicians became unsure of the foundational validity of infinitesimals. But since nonstandard analysis exactly provides the missing legitimacy, the original motivation for adopting epsilon-delta arguments appears to fall away.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "Analysis",
          "analysis"
        ],
        [
          "hyperreal number",
          "hyperreal number"
        ],
        [
          "infinitesimal",
          "infinitesimal"
        ],
        [
          "differential",
          "differential"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Nichtstandardanalysis"
    }
  ],
  "word": "nonstandard analysis"
}