- #1

- 207

- 0

## 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.

## 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.