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Universal set : ウィキペディア英語版 | Universal set
In set theory, a universal set is a set which contains all objects, including itself.〔Forster 1995 p. 1.〕 In set theory as usually formulated, the conception of a universal set leads to a paradox (Russell's paradox) and is consequently not allowed. However, some non-standard variants of set theory include a universal set. It is often symbolized by the Greek letter xi. ==Reasons for nonexistence== Zermelo–Fraenkel set theory and related set theories, which are based on the idea of the cumulative hierarchy, do not allow for the existence of a universal set. Its existence would cause paradoxes which would make the theory inconsistent.
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「Universal set」の詳細全文を読む
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