1. The problem statement, all variables and given/known data Let A be a set of positive real numbers. Assume that there is a bound b such that the sum of any finite subset of A is less than b. Show that A is countable. 3. The attempt at a solution So, my first question is what would be a better approach? Trying to find a function from the natural numbers to A or supposing that A is not countable and deriving a contradiction. I'm a little stumped on how to start the construction of such a function.