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

[irony of truth]

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"?

 

[quasar987]

Seems so to me.

 

[Maxos]

Well, a "limit point" (I cannot find the precise meaning of the phrase) has to be an accumulation point for the domain, then...

 

[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.

 

[rachmaninoff]

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.