For a finite set $X$, we write $\sum X$ to be the sum of all the numbers in $X$. Suppose we have a set $S \subseteq \mathbb{R}$ such that $-100\le \sum X \le 100$ for all finite subsets $X \subseteq S$. How to show that $S$ is countable?
I do not really know where to begin. Hints would be nice. Thank you!