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**1. Homework Statement**

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.