(p12 Exercise 1.3.6 Understanding Analysis, Abbott) I try to determine the $\inf$ and $\sup$ of the following sets. Can you tell me if my result is correct? I am also interested in how to compute it. Now I only determined it by varying the values. 

Define sets $B= \{ {n \over n + m } : m,n \in \mathbb N\}$, $C = \{ {n \over 2n + 1} :n \in \mathbb N\} $, $D= \{ {n \over m} : n , m \in \mathbb N , n+m \le 10 \}$. The $\inf$ and $\sup$ is:

$\inf B =0, \sup B = 1$ , 

$\inf C = 0, \sup C = {1 \over 2}$, 

$\inf D = 0, \sup D = \infty$.