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Math Help - Showing that the powerset of odd numbers is uncountable

  1. #1
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    Showing that the powerset of odd numbers is uncountable

    I have already proved that the powerset of the natural numbers is uncountable. To show that P(M) is uncountable where M={n∈N | 2 divides n) I think I need to construct a bijection between P(N) and P(M)? I'm unsure of exactly how to achieve this - I can only imagine a bijection between N and M.

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by StaryNight View Post
    I have already proved that the powerset of the natural numbers is uncountable. To show that P(M) is uncountable where M={n∈N | 2 divides n) I think I need to construct a bijection between P(N) and P(M)? I'm unsure of exactly how to achieve this - I can only imagine a bijection between N and M.
    This is a well-known result: If A\sim B, equipotent, then .
    After all there is a bijection .
    So result follows that subsets of A biject to subsets of B.
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  3. #3
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    Let f be a bijection between M and N.

    Define g:PM -> PN by

    g(x) = the f-image of x.

    It's trivial to verify that g is a bijection onto PN.
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