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- Pigeonhole_principle abstract "In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. This theorem is exemplified in real-life by truisms like "there must be at least two left gloves or two right gloves in a group of three gloves". It is an example of a counting argument, and despite seeming intuitive it can be used to demonstrate possibly unexpected results; for example, that two people in London have the same number of hairs on their heads (see below).The first formalization of the idea is believed to have been made by Peter Gustav Lejeune Dirichlet in 1834 under the name Schubfachprinzip ("drawer principle" or "shelf principle"). For this reason it is also commonly called Dirichlet's box principle, Dirichlet's drawer principle or simply "Dirichlet principle" — a name that could also refer to the minimum principle for harmonic functions. The original "drawer" name is still in use in French ("principe des tiroirs"), Polish ("zasada szufladkowa"), Hungarian ("skatulyaelv"), Italian ("principio dei cassetti"), German ("Schubfachprinzip"), Danish ("Skuffeprincippet"), and Chinese ("抽屉原理").Though the most straightforward application is to finite sets (such as pigeons and boxes), it is also used with infinite sets that cannot be put into one-to-one correspondence. To do so requires the formal statement of the pigeonhole principle, which is "there does not exist an injective function on finite sets whose codomain is smaller than its domain". Advanced mathematical proofs like Siegel's lemma build upon this more general concept.".
- Pigeonhole_principle thumbnail TooManyPigeons.jpg?width=300.
- Pigeonhole_principle wikiPageExternalLink mathword.html.
- Pigeonhole_principle wikiPageExternalLink p.html.
- Pigeonhole_principle wikiPageExternalLink 16-fun-applications-of-the-pigeonhole-principle.
- Pigeonhole_principle wikiPageExternalLink EWD980.html.
- Pigeonhole_principle wikiPageExternalLink pigeon.shtml.
- Pigeonhole_principle wikiPageExternalLink proofs.pigeonhole.html.
- Pigeonhole_principle wikiPageID "54217".
- Pigeonhole_principle wikiPageRevisionID "600878488".
- Pigeonhole_principle hasPhotoCollection Pigeonhole_principle.
- Pigeonhole_principle id "p/d032800".
- Pigeonhole_principle title "Dirichlet box principle".
- Pigeonhole_principle subject Category:Combinatorics.
- Pigeonhole_principle subject Category:Mathematical_principles.
- Pigeonhole_principle subject Category:Ramsey_theory.
- Pigeonhole_principle subject Category:Theorems_in_discrete_mathematics.
- Pigeonhole_principle type Abstraction100002137.
- Pigeonhole_principle type Cognition100023271.
- Pigeonhole_principle type Communication100033020.
- Pigeonhole_principle type Content105809192.
- Pigeonhole_principle type Generalization105913275.
- Pigeonhole_principle type Idea105833840.
- Pigeonhole_principle type MathematicalPrinciples.
- Pigeonhole_principle type Message106598915.
- Pigeonhole_principle type Principle105913538.
- Pigeonhole_principle type Proposition106750804.
- Pigeonhole_principle type PsychologicalFeature100023100.
- Pigeonhole_principle type Statement106722453.
- Pigeonhole_principle type Theorem106752293.
- Pigeonhole_principle type TheoremsInDiscreteMathematics.
- Pigeonhole_principle comment "In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. This theorem is exemplified in real-life by truisms like "there must be at least two left gloves or two right gloves in a group of three gloves".".
- Pigeonhole_principle label "Duiventilprincipe".
- Pigeonhole_principle label "Pigeonhole principle".
- Pigeonhole_principle label "Principe des tiroirs".
- Pigeonhole_principle label "Principio dei cassetti".
- Pigeonhole_principle label "Principio del palomar".
- Pigeonhole_principle label "Princípio da casa dos pombos".
- Pigeonhole_principle label "Schubfachprinzip".
- Pigeonhole_principle label "Zasada szufladkowa Dirichleta".
- Pigeonhole_principle label "Принцип Дирихле (комбинаторика)".
- Pigeonhole_principle label "مبدأ برج الحمام".
- Pigeonhole_principle label "鳩の巣原理".
- Pigeonhole_principle label "鴿巢原理".
- Pigeonhole_principle sameAs Dirichletův_princip.
- Pigeonhole_principle sameAs Schubfachprinzip.
- Pigeonhole_principle sameAs Principio_del_palomar.
- Pigeonhole_principle sameAs Usategi_printzipio.
- Pigeonhole_principle sameAs Principe_des_tiroirs.
- Pigeonhole_principle sameAs Prinsip_Rumah_Burung.
- Pigeonhole_principle sameAs Principio_dei_cassetti.
- Pigeonhole_principle sameAs 鳩の巣原理.
- Pigeonhole_principle sameAs 비둘기집_원리.
- Pigeonhole_principle sameAs Duiventilprincipe.
- Pigeonhole_principle sameAs Zasada_szufladkowa_Dirichleta.
- Pigeonhole_principle sameAs Princípio_da_casa_dos_pombos.
- Pigeonhole_principle sameAs m.0f59r.
- Pigeonhole_principle sameAs Q188276.
- Pigeonhole_principle sameAs Q188276.
- Pigeonhole_principle sameAs Pigeonhole_principle.
- Pigeonhole_principle wasDerivedFrom Pigeonhole_principle?oldid=600878488.
- Pigeonhole_principle depiction TooManyPigeons.jpg.
- Pigeonhole_principle isPrimaryTopicOf Pigeonhole_principle.
