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Finding Cluster Points/Accumulation Points

brooklysuse

New member
Jun 26, 2019
4
Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}. Justify your answer with
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.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,490
Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}.
I believe 0 is a cluster point
Hmm, I believe \(\displaystyle \frac{(-1)n}{n}=-1\).
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,697
Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}. Justify your answer with
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.
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.)