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

  • #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"?
 

Answers and Replies

  • #2
quasar987
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Seems so to me.
 
  • #3
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Well, a "limit point" (I cannot find the precise meaning of the phrase) has to be an accumulation point for the domain, then....
 
  • #4
MalleusScientiarum
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.
 
  • #5
rachmaninoff
MalleusScientiarum said:
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.
Not necessary.
 

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