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Awatmath.2030 net.math utcsrgv!utzoo!decvax!watmath!bstempleton Wed Mar 17 13:18:30 1982 Paradox in set theory Consider : "The set of all sets that are not members of themselves"

This set is not all sets clearly, since some sets like the set of ideas and the set of mathematical objects are members of themselves.

The set is not empty, because the set of Vax computers is not a member of itself.

Yet the set is a paradox, for if it is a member of itself, then it is not a member of itself, and if it is not a member of itself, then it is a member of itself.

-The nasty thing about this paradox is that you CAN'T explain it with conventional set theory as far as I know.

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