A set $A = \left\{(-1)^n + \frac{1}{m} : n,m \in \Bbb N\right\} \cup \{-1\}$ is given.
a) I shall find out and justify what the supremum an infimum is.
b) Is the sup a maximum or the inf a minimum.
a) For the sup, I find out $n=2$ and $m=1$ because then I have $1+1=2$. For the inf, I have $\displaystyle \lim _{m\to\infty} (1/m) = 0$ and $n = \text{odd number} \implies 0-1=-1$.
Now my questions are: Is that correct? How can I now find out if there is a max or min? Can I say for the sup that $2$ and $1$ are elements of $\Bbb N$ so the sup is a max and for the inf same? And what about the $\{-1\}$ in the set, what does this $\{-1\}$ mean for the inf, sup, min and max?