1. Mar 20, 2007 #1

   Willy_Will

   

   Hi all,
   
   Im having trouble with this problem, I dont know where to begin.
   
   Suppose that Ä is a nested family of sets.
   
   1. Prove that U (from k=1 to infite) A(sub k) = A(sub l)
   
   2. Prove that ∩ (from k=1 to n) A(sub k) = A(sub n)
   
   
   Thanks in advace mathematicians!
   
   -William

    

   Willy_Will, Mar 20, 2007
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3. Mar 20, 2007 #2

   ZioX

   

   1) To show that they are equal you must show that they are subsets of one another.
   
   2) If x is in the union of a collection of sets, what does this mean?
   
   3) If x is in the intersection of a collection of sets, what does this mean?
   
   4) You have to use the assumption of nested somewhere.
   
   5) If A is a subset of B what can you say about A n b?
   
   6) If A is a subset of B what can you say about A U B?

    

   ZioX, Mar 20, 2007

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