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Oct 15, 2010 at 4:29 comment added Pete L. Clark I upvoted this as well and agree with Ricky Demer's comment. @spoon47: "arbitrary" is not a quantifier. It turns out you meant to to ask for sets $A$ and $B$ which had this property for all $x,y$ with $x < y$. I recommend that you edit the question to clarify this.
Oct 14, 2010 at 6:34 comment added spoon47 Should have clarified: (x,y) should be arbitrary. (Technically, this follows from the construction that the sets each have infinite measure).
Oct 14, 2010 at 6:31 comment added user5810 +1 for showing the OP the importance of quantifiers.
Oct 14, 2010 at 6:21 history answered brian CC BY-SA 2.5