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Math Help - Find a point set P whose first and second derived sets are nonempty and different fro

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    Find a point set P whose first and second derived sets are nonempty and different fro

    Find a point set P whose first and second derived sets are nonempty and different from P and find each other.
    I have a lot of trouble in finding this point set P.
    I tried P={sin n}, and first derived set of P ={the real numbers on the interval [-1,1]}, but thus the second derived set = the first derived set.
    Anybody could help me with this?
    Thankss a lottt!!!
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    Quote Originally Posted by suna View Post
    Find a point set P whose first and second derived sets are nonempty and different from P and from each other.
    How about the set \{(1/m,1/n)\in\mathbb{R}^2:m,n\in\mathbb{N}\}?
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    Quote Originally Posted by Opalg View Post
    How about the set \{(1/m,1/n)\in\mathbb{R}^2:m,n\in\mathbb{N}\}?
    Thankyou, but I think the 1st derived set of this set is {0,0}, so the second derived set of it is {0}
    Are they different?
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    Quote Originally Posted by Opalg View Post
    How about the set A= \{(1/m,1/n)\in\mathbb{R}^2:m,n\in\mathbb{N}\}?
    Quote Originally Posted by suna View Post
    Thankyou, but I think the 1st derived set of this set is {0,0}, so the second derived set of it is {0}
    Are they different?
    Would \left( {\frac{1}{2},0} \right) \in A'\,\& \,\left( {0,\frac{1}{4}} \right) \in A'? Well of course they do!
    So what is {A''}?
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