Some (but not all) sums of rational numbers gives us 1 as a result. For instance: $$\frac12 + \frac12 = 1$$ $$\frac13 + \frac23 = 1$$ $$\frac37 + \frac{3}{14} + \frac{5}{14} = 1$$ Is the set of all of these sums countable? Sums that differ just by their addends ordering are the same. So $(\fr...