find the number of limit points of the set{$ \frac{1}{m} +\frac{1}{n}:m,n \in \Bbb N$} 
Problem:find the number of limit points {$ \frac{1}{m} +\frac{1}{n}:m,n \in \Bbb N$}
Solution:$$ \lim_{(m,n)\to\infty}\frac{1}{m} +\frac{1}{n}$$
$=0$
So there is one limit point

Am I doing right ?
Answer is infinitely many limit points

the limit points are only  $\{\frac{1}{n}: n \in \mathbb N\} \cup 0$
as $1+\frac{1}{n} \rightarrow 1$ 
similarly $\frac{1}{m}+\frac{1}{n}\rightarrow \frac{1}{m}$ where $m$ is fixed and $n$ varies.
