# cluster points

• Nov 25th 2012, 09:06 PM
duckyone
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+}
• Nov 26th 2012, 03:21 AM
coolge
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
• Nov 26th 2012, 03:37 AM
Plato
Re: cluster points
Quote:

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.