If I use $\displaystyle x\leq\frac{k}{2^n}$ to show E is nonempty and bounded above, then E has a supremum. What would I use to show: If E is nonempty and bounded below, then E has an infimum. Would $\displaystyle x\geq\frac{k}{2^n}$ work? When I tried this the induction part doesn't make sense to me. For example by induction, then, there exists integers $\displaystyle k_n$ least in $\displaystyle A_n$ such that $\displaystyle k_o \leq \frac{k_1}{2} \leq \frac{k_2}{4} \leq ... \leq \frac{k_n}{2^n} \leq ...$ and to me that doesn't seem to make sense for something bounded below.