Are the following identifications correct? I am particularly unsure about (b).
(a). $\left\{m/n : m,n\in\mathbf{N}\text{ with }m<n\right\}$
Solution. Letting $A$ denote the above set, $\inf A=0$ and $\sup A = 1$.
(b). $\left\{(-1)^m/n : m,n\in\mathbf{N}\right\}$
Solution. Letting $B$ denote the above set, $\inf B=0$ and $\sup B = 1$
(c). $\left\{n/(3n+1) : n\in\mathbf{N}\right\}$
Solution. Letting $C$ denote the above set, $\inf C = \frac{1}{4}$ and $\sup C = \frac{1}{3}$.
(d). $\left\{m/(m+n) : m,n\in\mathbf{N}\right\}$
Solution. Letting $D$ denote the above set, $\inf D = 0$ and $\sup D = 1$.