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:''"Bounded" and "boundary" are distinct concepts; for the latter see boundary (topology). A circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded. The word bounded makes no sense in a general topological space, without a metric. == Definition == A set ''S'' of real numbers is called ''bounded from above'' if there is a real number ''k'' such that ''k'' ≥ '' s'' for all ''s'' in ''S''. The number ''k'' is called an upper bound of ''S''. The terms ''bounded from below'' and lower bound are similarly defined. A set ''S'' is bounded if it has both upper and lower bounds. Therefore, a set of real numbers is bounded if it is contained in a finite interval. 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「bounded set」の詳細全文を読む スポンサード リンク
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