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[limit point proof]: L(aub)=l(a)ul(b)

  1. Sep 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Let L(X) denote the set of limit points of a set X in R^n. How do I prove that L(AUB)=L(A)UL(B)?

    3. The attempt at a solution
    I know that I have to prove that both sides are subsets of each other, but I have no clue how to start...
     
    Last edited: Sep 26, 2011
  2. jcsd
  3. Sep 26, 2011 #2

    CompuChip

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    So the standard form of an argument goes like: let [itex]x \in L(A \cup B)[/itex]. Then... what does x satisfy (i.e. what is the definition of a limit point of a set X)?
     
  4. Sep 26, 2011 #3
    Remember that if you want to prove a sets equality, you have to prove both inclusions. En this case, there is a trivial inclusion (which?).
     
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