Thread: 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+}

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

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 then

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