Paradoxical set

In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is a partitioning of the set into two subsets, along with an appropriate group of functions that operate on some universe (of which the set in question is a subset), such that each partition can be mapped back onto the entire set using only finitely many distinct functions (or compositions thereof) to accomplish the mapping. Since a paradoxical set as defined requires a suitable group $G$ , it is said to be $G$ -paradoxical, or paradoxical with respect to $G$ .

单词	Paradoxical set
释义	Paradoxical set 英语百科 Paradoxical set In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is a partitioning of the set into two subsets, along with an appropriate group of functions that operate on some universe (of which the set in question is a subset), such that each partition can be mapped back onto the entire set using only finitely many distinct functions (or compositions thereof) to accomplish the mapping. Since a paradoxical set as defined requires a suitable group $G$ , it is said to be $G$ -paradoxical, or paradoxical with respect to $G$ .
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