The set S contains some real numbers, according to the following three rules.

1) 1/1 is in S.

2) If a/b is in S, where a/b is written in lowest terms (that is, a and b have highest common factor 1), then b/2a is in S.

3) If a/b and c/d are in S, where they are written in lowest terms, then a+c/b+d is in S.

These rules are exhaustive: If these rules do not imply that a number is in S, then that number is not in S. Can you describe which numbers are in S?