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Analysis question

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that each of A and B is a set such that:
    (a) A is a subset of [0,1], B is a subset of [0,1]
    (b) Neither of A or B is empty
    (c) 0 (zero) is an element of A
    (d) The union of A & B = [0,1]
    (e) A & B are disjoint
    (f) A contains no limit points of B.

    Then, B contains a limit point of A.

    2. Relevant equations
    None

    3. The attempt at a solution
    Not sure where to go with it...
     
  2. jcsd
  3. Apr 19, 2010 #2
    If [tex]A[/tex] contains no limit point of [tex]B[/tex], then what kind of points does [tex]A[/tex] consist of? (What must [tex]A[/tex] look like near [tex]0[/tex]? How far from [tex]0[/tex] can you "push" this appearance?)
     
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