Find all accumulation points of the following set in R^2 with the usual metric.
{ (1/n+m , 1/n + 1/m) : n, m ∈ N }
If anyone helps me, I will be thankful.
I think that both poster and Mathstud28 need to consider the makeup of the set
.
Note that the set is in the quarter closed disk, centered at (0,0) with radius .
The point furthest from the origin is happens when .
If we let then we get the points .
Now, we must remind ourselves of the definition of accumulation point.
If is an accumulation point of then must be the limit of a sequence of distinct points in .
Again think about letting then we get the points as .
Does that help you to think about this set?