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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pigeonhole principle ： ウィキペディア英語版 Pigeonhole principle In mathematics, the pigeonhole principle states that if items are put into containers, with , 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's principle"〔Jeff Miller, Peter Flor, Gunnar Berg, and Julio González Cabillón. "(Pigeonhole principle )". In Jeff Miller (ed.) ''(Earliest Known Uses of Some of the Words of Mathematics )''. Electronic document, retrieved November 11, 2006〕 — 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"), Bulgarian ("принцип на чекмеджетата"), Turkish ("çekmece ilkesi"), Hungarian ("skatulyaelv"), Italian ("principio dei cassetti"), German ("Schubfachprinzip"), Danish ("Skuffeprincippet"), and Chinese ("抽屉原理"). The principle has several generalizations and can be stated in various ways. In a more quantified version: for natural numbers and , if objects are distributed among sets, then the pigeonhole principle asserts that at least one of the sets will contain at least objects. For arbitrary and this generalizes to , where is the floor function. 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 whose codomain is smaller than its domain"''. Advanced mathematical proofs like Siegel's lemma build upon this more general concept. == Examples == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pigeonhole principle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.