Let $N$ be the set of positive integers. For all $n \in N$,let $f_n = (n+1)^{1/3} - n^{1/3}$ and $A = \{n \in N : f_{n+1} < \frac{1}{3(n+1)^{2/3}} < f_n\}$. Then,
- A$A = N$
- B$A$ is a finite set
- Cthe complement of $A$ in $N$ is nonempty,but finite
- D$A$ and its complement in $N$ are both infinite
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