Hi,

Here I am reading Rudin's Book(3rd).

I encountered some problems inTheorem 2.20, page32.

Theorem 2.20

If p is a limit point of a set E, then every neighborhood of p contains infinitely many points of E.

By intutition or imagination, I can understand the theorem, but I just don't understand why it says,

"The neighborhoodNr(p)contains no pointqofEsuch thatp=/=q(not equal), so thatpis not a limit point ofE." in the proof.

I think it would be thatNr(p)contains someqwhenris in some range, but in other range ofr, there is noqofEsuch thatp=/=q. In other words, not every neighborhood ofpcontains aqofE, such thatp=/=q.

Is there anyone who has the book on hands?