"Peano arithmetic" meaning in English

See Peano arithmetic in All languages combined, or Wiktionary

Noun

Forms: Peano arithmetics [plural]
Etymology: Named after Italian mathematician Giuseppe Peano (1858–1932). Etymology templates: {{named-after/list|mathematician||||}} mathematician, {{!}} |, {{lang|en|Giuseppe Peano}} Giuseppe Peano, {{named-after|en|Giuseppe Peano|born=1858|died=1932|nat=Italian|occ=mathematician|wplink==}} Named after Italian mathematician Giuseppe Peano (1858–1932) Head templates: {{en-noun|~}} Peano arithmetic (countable and uncountable, plural Peano arithmetics)
  1. (logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction. Wikipedia link: Peano arithmetic Tags: countable, uncountable Categories (topical): Logic Related terms: Presburger arithmetic Translations (Translations): Peanon aritmetiikka (Finnish), Peanoarithmetik [feminine] (German), arytmetyka Peana [feminine] (Polish)
    Sense id: en-Peano_arithmetic-en-noun-TlRWJf~x Categories (other): English entries with incorrect language header Topics: human-sciences, logic, mathematics, philosophy, sciences

Inflected forms

Alternative forms

Download JSON data for Peano arithmetic meaning in English (2.4kB)

{
  "etymology_templates": [
    {
      "args": {
        "1": "mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano"
      },
      "expansion": "Giuseppe Peano",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano",
        "born": "1858",
        "died": "1932",
        "nat": "Italian",
        "occ": "mathematician",
        "wplink": "="
      },
      "expansion": "Named after Italian mathematician Giuseppe Peano (1858–1932)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after Italian mathematician Giuseppe Peano (1858–1932).",
  "forms": [
    {
      "form": "Peano arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "Peano arithmetic (countable and uncountable, plural Peano arithmetics)",
      "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"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "id": "en-Peano_arithmetic-en-noun-TlRWJf~x",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "first-order logic",
          "first-order logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "successor",
          "successor"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "related": [
        {
          "word": "Presburger arithmetic"
        }
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "Peanon aritmetiikka"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Peanoarithmetik"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "arytmetyka Peana"
        }
      ],
      "wikipedia": [
        "Peano arithmetic"
      ]
    }
  ],
  "word": "Peano arithmetic"
}
{
  "etymology_templates": [
    {
      "args": {
        "1": "mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano"
      },
      "expansion": "Giuseppe Peano",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Giuseppe Peano",
        "born": "1858",
        "died": "1932",
        "nat": "Italian",
        "occ": "mathematician",
        "wplink": "="
      },
      "expansion": "Named after Italian mathematician Giuseppe Peano (1858–1932)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after Italian mathematician Giuseppe Peano (1858–1932).",
  "forms": [
    {
      "form": "Peano arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "Peano arithmetic (countable and uncountable, plural Peano arithmetics)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Presburger arithmetic"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English uncountable nouns",
        "Translation table header lacks gloss",
        "en:Logic"
      ],
      "glosses": [
        "A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "first-order logic",
          "first-order logic"
        ],
        [
          "natural number",
          "natural number"
        ],
        [
          "successor",
          "successor"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "wikipedia": [
        "Peano arithmetic"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "Peanon aritmetiikka"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Peanoarithmetik"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "arytmetyka Peana"
    }
  ],
  "word": "Peano arithmetic"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c 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.