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A156972
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Number of universes with n entities, exactly one being the empty set, which satisfy the Axiom of Extensionality (two sets are identical when they have the same elements) and are closed under taking subsets.
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0
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1, 2, 6, 60, 840, 18720, 559440, 22196160, 1092631680, 65768371200, 4703596128000, 393785778355200
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OFFSET
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1,2
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COMMENTS
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These universes need not satisfy the Power Set Axiom.
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LINKS
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EXAMPLE
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1 entity = 1 universe that consists of the empty set. 2 entities = 2 universes: when a = {{}}, when a = {a} on the other hand. 3 entities = 6 universes: a = {{}}, b = {a}; a = {{}}, b = {b}; and so on. 4 entities = 60 universes...
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CROSSREFS
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KEYWORD
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hard,nonn,nice,more
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AUTHOR
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Csabay Karoly (csabay58(AT)gmail.com), Feb 19 2009, Jun 14 2009, Mar 20 2010
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STATUS
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approved
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