# Math Help - cluster points

1. ## cluster points

So I have to prove the following but I have NO idea about cluster points. Could anyone help explain cluster points and help me prove this?

Show that 0 is a cluster point of S = {1/n: n is an elemnt of Z+}

2. ## Re: cluster points

Cluster points are also known as accumulation points. In this case you need to show that every neighborhood of 0 contains atleast one point of S. Then 0 will be a cluster/accumulation point of S. The cluster point need not have to be in the set S

3. ## Re: cluster points

Originally Posted by duckyone
So I have to prove the following but I have NO idea about cluster points. Could anyone help explain cluster points and help me prove this?
Show that 0 is a cluster point of S = {1/n: n is an elemnt of Z+}

Do you know that if $\delta>0$ then $(\exists n\in\mathbb{Z}^+)[1/n <\delta]~?$

If your class has not done that, then it is pointless to try this question.