Question

6. The set \( S \) contains some real numbers, according to the following three rules. (i) \( \frac{1}{1} \) is in \( S \). (ii) If \( \frac{a}{b} \) is in \( S \), where \( \frac{a}{b} \) is written in lowest terms (that is, \( a \) and \( b \) have highest common factor 1 ), then \( \frac{b}{2 a} \) is in \( S \). (iii) If \( \frac{a}{b} \) and \( \frac{c}{d} \) are in \( S \), where they are written in lowest terms, then \( \frac{a+c}{b+d} \) 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 \( S ? \)

          6. The set \( S \) contains some real numbers, according to the following three rules.
(i) \( \frac{1}{1} \) is in \( S \).
(ii) If \( \frac{a}{b} \) is in \( S \), where \( \frac{a}{b} \) is written in lowest terms (that is, \( a \) and \( b \) have highest common factor 1 ), then \( \frac{b}{2 a} \) is in \( S \).
(iii) If \( \frac{a}{b} \) and \( \frac{c}{d} \) are in \( S \), where they are written in lowest terms, then \( \frac{a+c}{b+d} \) 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 \( S ? \)

6. The set S contains some real numbers, according to the following three rules.
(i) (1)/(1) is in S.
(ii) 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)/(2 a) is in S.
(iii) 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 ?

Added by Abdullah U.

Question

Please give Ace some feedback