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In mathematics, a nonempty subset ''S'' of a group ''G'' is said to be symmetric if : where . In other words, ''S'' is symmetric if whenever . If ''S'' is a subset of a vector space, then ''S'' is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if . ==Examples== * In R, examples of symmetric sets are intervals of the type with , and the sets Z and . * Any vector subspace in a vector space is a symmetric set. * If ''S'' is any subset of a group, then and are symmetric sets. 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「Symmetric set」の詳細全文を読む スポンサード リンク
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