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Re: Russell's paradoxPosted by DickT on January 21, 2003 at 19:19:47: In Reply to: Russell's paradox posted by RocketMan on January 21, 2003 at 16:58:05: RocketMan, Have you come across the Spanish Barber? It was Russell's attempt to bring the paradox to the layman. In a certain Spanish town the barber (who is a man) shaves every man who does not shave himself. Who shaves the barber? So now. Some sets are members of themselves. For example the set of nonempty sets is a member of itself, because it is a nonempty set. Other sets are not members of themselves. For example the set of rusty anvils is not a member of itself since it is a set, not a rusty anvil. Consider then the set of all sets that are NOT members of themselves. Is it a member of itself? If it is, then it is like all the other members a set which is NOT a member of itself, so it cannot be a member of itself. Contradiction. Suppose it is NOT a member of itself, then by definition it IS a member of itself. Contradiction again. This sounds like a game to most of us, but it was deadly serious to Russell and the other early set theorists. They thought everything in math could be expressed through sets, and the fact that set theory could produce paradoxes was extremely shocking to them. Regards, Follow Ups: (Reload page to see most recent)
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