I stumbled upon Mr Russel's and Ernst Zermelo Paradox http://en.wikipedia.org/wiki/Russell%27s_paradox. According to wiki, Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox.
I understand that if a set R contains set - elements that are not members of them selfs, but because those sets are not members of them selfs, that means that R inherits the property of its contained elements the "none membership of them selfs"?
And then why it "must" contain it self. Why does that property of R has to be inherited by its child sets. I just can't get the way the mathematical mind works around this problem.
Thank you
