Charles Kincaid (1/6/2010)

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Given the set A which is a set of all sets that do not contain themselves as proper subsets, is set A in set A?

Believe it or not, there's a workaround to this problem!! Bertrand Russell, who dreamed up the paradox, tried to fix it by arranging sets in a heirarchy of "types". Later (by the time I studied math), this was simplified to a two-type heirarchy as follows:

A class is a collection of things. A set is a class that's a member of some class. This resolves the Russell paradox because the collection of all sets which are not members of themselves is a class but not a set.