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

1. Aug 11, 2005

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"?

2. Aug 11, 2005

quasar987

Seems so to me.

3. Aug 12, 2005

Maxos

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

4. Aug 12, 2005

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. Aug 12, 2005

rachmaninoff

Not necessary.