Consider a finite, nonempty set of powers of two that are greater than one. The sum of the reciprocals is between zero and one, and you can always expand any su

Consider a finite, nonempty set of powers of two that are greater than one. The sum of the reciprocals is between zero and one, and you can always expand any such set to another larger one, which will increase the sum of reciprocals but it will still be under one.