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In mathematics, a finite set is a set that has a finite number of elements. For example, : is a finite set with five elements. The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: : Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. == Definition and terminology == Formally, a set is called finite if there exists a bijection : for some natural number . The number is the set's cardinality, denoted as ||. The empty set is a 2-subset of it. 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「finite set」の詳細全文を読む スポンサード リンク
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