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February 8th, 2016, 09:19 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,537 Thanks: 108  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$x=0 But x is circular. Last edited by zylo; February 8th, 2016 at 09:25 AM. Reason: replace b with y to match AR 
February 8th, 2016, 09:54 AM  #2 
Member Joined: Sep 2013 Posts: 33 Thanks: 0 
Try this form : For all nonempty x and y in x, any z in x is not in y. 
February 8th, 2016, 11:09 AM  #3 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,537 Thanks: 108 
Ref: Axiom of Regularity is wrong x={y,{x}}, y∩x=0 members of x: y,{x} No member of y is a member of x. If A={b,c} and d$\displaystyle \in$c, d$\displaystyle \notin$A Last edited by zylo; February 8th, 2016 at 11:31 AM. 

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