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Math Help - Set of all sets paradox

  1. #1
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    Set of all sets paradox

    Let R = {X : X is a set and X is not an element of X }. Is the statement R is an element of R true or false?

    Thanks for all the help!
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  2. #2
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    Quote Originally Posted by jstarks44444 View Post
    Let R = {X : X is a set and X is not an element of X }. Is the statement R is an element of R true or false?
    If R\in R then R\notin R.
    If R\notin R then R\in R.
    What do you think?
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  3. #3
    Super Member TheChaz's Avatar
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    I think I just pooped my pants!
    But seriously...
    j, you basically have the answer already (even before considering Plato's explicit argument) that this is a paradox. If this is part of an assignment, you should elaborate a bit on the above reasoning (R in R --> R not in R, etc) and maybe add some "original" commentary.
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    Forum Admin topsquark's Avatar
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