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Math Help - ZF Axiom of Regularity and Russell's Paradox

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    ZF Axiom of Regularity and Russell's Paradox

    Today in my junior level discrete math class, my professor taught the Zermelo-Fraenkel axioms. He then when on to say that the axiom of regularity resolves Russell's paradox. Not taking anything at face value, I decided to investigate and found that this was indeed incorrect. I attempted to explain to him why this is incorrect, but he could not accept the truth. I showed him this link:

    [HTML]http://www.statemaster.com/encyclopedia/Axiom-of-regularity[/HTML]

    To which he replied, "I am just using the curriculum that I was given." For someone with a PHD in CS, I found this quite amusing. Why is this incorrect assumption so widespread? If the link I provided is correct, then this assumption is due to an misunderstanding of the definition of an axiom. Should I dispute this matter further, or just stay quiet? Also, can anyone recommend any good books which cover ZF axioms and type theory?
    Last edited by aaronrj; September 17th 2009 at 04:15 PM. Reason: typo
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