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February 8th, 2016, 09:19 AM   #1
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Zermelo Frankel Axiom of Regularity

Axiom of Regularity: For any set x$\displaystyle \neq$0 there is a member y of x such that y$\displaystyle \cap$x=0.
x={y,{x}}, y$\displaystyle \cap$x=0
But x is circular.

Last edited by zylo; February 8th, 2016 at 09:25 AM. Reason: replace b with y to match AR
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February 8th, 2016, 09:54 AM   #2
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Try this form :

For all nonempty x and y in x, any z in x is not in y.
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February 8th, 2016, 11:09 AM   #3
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Ref:
Axiom of Regularity is wrong


x={y,{x}}, y∩x=0

members of x: y,{x}
No member of y is a member of x.

If A={b,c} and d$\displaystyle \in$c, d$\displaystyle \notin$A

Last edited by zylo; February 8th, 2016 at 11:31 AM.
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