"pigeonhole principle" meaning in All languages combined

{
  "etymology_text": "From the commonly used expository example that if n+1 pigeons are placed in n pigeonholes, at least one pigeonhole must contain two (or more) pigeons.",
  "forms": [
    {
      "form": "pigeonhole principles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "pigeonhole principle (countable and uncountable, plural pigeonhole principles)",
      "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"
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          "source": "w"
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        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Polish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Slovak translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1993, David Gries, Fred B. Schneider, A Logical Approach to Discrete Math, Springer, page 355:",
          "text": "The pigeonhole principle is usually stated as follows.\n(16.43) If more than n pigeons are placed in n holes, at least one hole will contain more than one pigeon.\nThe pigeonhole principle is obvious, and one may wonder what it has to do with computer science or mathematics.",
          "type": "quote"
        },
        {
          "ref": "2009, John Harris, Jeffry L. Hirst, Michael Mossinghoff, Combinatorics and Graph Theory, Springer, page 313, Of course our list of pigeonhole principles is not all inclusive. For example, more set theoretic pigeonhole principles are given in [72]. Corollary 3.31 (Ultimate Pigeonhole Principle). The following are equivalent",
          "text": "1. κ is a regular cardinal.\n2. If we put κ pigeons into λ < κ pigeonholes, then some pigeonhole must contain κ pigeons."
        },
        {
          "text": "2012, Dov M. Gabbay, Akihiro Kanamori, John Woods (editors), Handbook of the History of Logic: Volume 6: Sets and Extensions in the Twentieth Century, Elevier (North-Holland), page 325,\nAs we turn to look at various pigeonhole principles and how they are used to prove partition theorems, particularly for pairs, we keep in mind the slogan that is embedded in the Motzkin quote: complete disorder is impossible."
        }
      ],
      "glosses": [
        "The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence)."
      ],
      "id": "en-pigeonhole_principle-en-noun-nE34iP2v",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "set",
          "set"
        ],
        [
          "element",
          "element"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "cardinality",
          "cardinality"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence)."
      ],
      "synonyms": [
        {
          "sense": "theorem limiting size of codomains",
          "word": "Dirichlet's box principle"
        },
        {
          "sense": "theorem limiting size of codomains",
          "word": "Dirichlet's drawer principle"
        }
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "combinatorial theorem",
          "word": "kyyhkyslakkaperiaate"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "combinatorial theorem",
          "tags": [
            "feminine"
          ],
          "word": "zasada szufladkowa (Dirichleta)"
        },
        {
          "code": "sk",
          "lang": "Slovak",
          "sense": "combinatorial theorem",
          "tags": [
            "masculine"
          ],
          "word": "Dirichletov princíp"
        }
      ]
    }
  ],
  "word": "pigeonhole principle"
}

{
  "etymology_text": "From the commonly used expository example that if n+1 pigeons are placed in n pigeonholes, at least one pigeonhole must contain two (or more) pigeons.",
  "forms": [
    {
      "form": "pigeonhole principles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "pigeonhole principle (countable and uncountable, plural pigeonhole principles)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Finnish translations",
        "Terms with Polish translations",
        "Terms with Slovak translations",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1993, David Gries, Fred B. Schneider, A Logical Approach to Discrete Math, Springer, page 355:",
          "text": "The pigeonhole principle is usually stated as follows.\n(16.43) If more than n pigeons are placed in n holes, at least one hole will contain more than one pigeon.\nThe pigeonhole principle is obvious, and one may wonder what it has to do with computer science or mathematics.",
          "type": "quote"
        },
        {
          "ref": "2009, John Harris, Jeffry L. Hirst, Michael Mossinghoff, Combinatorics and Graph Theory, Springer, page 313, Of course our list of pigeonhole principles is not all inclusive. For example, more set theoretic pigeonhole principles are given in [72]. Corollary 3.31 (Ultimate Pigeonhole Principle). The following are equivalent",
          "text": "1. κ is a regular cardinal.\n2. If we put κ pigeons into λ < κ pigeonholes, then some pigeonhole must contain κ pigeons."
        },
        {
          "text": "2012, Dov M. Gabbay, Akihiro Kanamori, John Woods (editors), Handbook of the History of Logic: Volume 6: Sets and Extensions in the Twentieth Century, Elevier (North-Holland), page 325,\nAs we turn to look at various pigeonhole principles and how they are used to prove partition theorems, particularly for pairs, we keep in mind the slogan that is embedded in the Motzkin quote: complete disorder is impossible."
        }
      ],
      "glosses": [
        "The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "partition",
          "partition"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "set",
          "set"
        ],
        [
          "element",
          "element"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "cardinality",
          "cardinality"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence)."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "theorem limiting size of codomains",
      "word": "Dirichlet's box principle"
    },
    {
      "sense": "theorem limiting size of codomains",
      "word": "Dirichlet's drawer principle"
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "combinatorial theorem",
      "word": "kyyhkyslakkaperiaate"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "combinatorial theorem",
      "tags": [
        "feminine"
      ],
      "word": "zasada szufladkowa (Dirichleta)"
    },
    {
      "code": "sk",
      "lang": "Slovak",
      "sense": "combinatorial theorem",
      "tags": [
        "masculine"
      ],
      "word": "Dirichletov princíp"
    }
  ],
  "word": "pigeonhole principle"
}