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If x is an accumulation point of set S and e >0

  1. Aug 11, 2005 #1
    If I were proving that "if x is an accumulation point of set S and e >0, then there are infinite number of points within e of x", is it exactly the same as saying "if x is a limit point of set S, then every neighborhood of x contains infinitely many points of S"?
     
  2. jcsd
  3. Aug 11, 2005 #2

    quasar987

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    Seems so to me.
     
  4. Aug 12, 2005 #3
    Well, a "limit point" (I cannot find the precise meaning of the phrase) has to be an accumulation point for the domain, then....
     
  5. Aug 12, 2005 #4
    As I recall an accumulation point is a point in the set A where any neighborhood of x has at least one other point in A that is not x.
     
  6. Aug 12, 2005 #5
    Not necessary.
     
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