- Thread starter
- #1

#### brooklysuse

##### New member

- Jun 26, 2019

- 4

proof.

I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not.

Any quick help would be appreciated. Thanks.

- Thread starter brooklysuse
- Start date

- Thread starter
- #1

- Jun 26, 2019

- 4

proof.

I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not.

Any quick help would be appreciated. Thanks.

- Jan 30, 2012

- 2,489

Hmm, I believe \(\displaystyle \frac{(-1)n}{n}=-1\).Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}.

I believe 0 is a cluster point

- Moderator
- #3

- Feb 7, 2012

- 2,681

I guess you mean $A := \{(−1)^n/n : n \in \Bbb{N}\}$. You are correct that $0$ is the only cluster point. To prove it, you will need to use the definition of a cluster point, which is ... ? (Start from there.)

proof.

I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not.

Any quick help would be appreciated. Thanks.