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 February 8th, 2016, 10:19 AM #1 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,641 Thanks: 119 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$x=0 But x is circular. Last edited by zylo; February 8th, 2016 at 10:25 AM. Reason: replace b with y to match AR
 February 8th, 2016, 10:54 AM #2 Member   Joined: Sep 2013 Posts: 33 Thanks: 0 Try this form : For all nonempty x and y in x, any z in x is not in y.
 February 8th, 2016, 12:09 PM #3 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,641 Thanks: 119 Ref: Axiom of Regularity is wrong x={y,{x}}, y∩x=0 members of x: y,{x} No member of y is a member of x. If A={b,c} and d$\displaystyle \in$c, d$\displaystyle \notin$A Last edited by zylo; February 8th, 2016 at 12:31 PM.

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### frankel axiom

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