I am a little confused by this question: Suppose , Prove that .

By definition, I know that but not . I believe only when that it can be a subset of . I am right?

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- Oct 18th 2010, 08:45 AMnoviceSubset of a Power set
I am a little confused by this question: Suppose , Prove that .

By definition, I know that but not . I believe only when that it can be a subset of . I am right? - Oct 18th 2010, 09:35 AMemakarov
In general, it is not the case that ; however, it is possible. Such sets are called transitive. Suppose . Then for every , , i.e., . This in turn means that for every , , which explains the name.

Other examples include , and other von Neumann ordinals.