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Math Help - onto funciton

  1. #1
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    onto funciton

    let x be a set and P(x) is one of the power sets of x,
    show that there is no onto function which is from x to P(x).
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  2. #2
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    Suppose that f:X \mapsto P(X) is any mapping from a set to its power set.
    Now define A = \left\{ {y \in X:y \notin f(y)} \right\}. Clearly A \in P(X).
    If f were a surjection then \left( {\exists a \in X} \right)\left[ {f(a) = A} \right].
    Work with until you see the contradiction
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