lowest terms (that is, a and b have highest common factor 1), then b/2a 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? For example, by (i), 1/1 is in S. By (ii), since 1/1 is in S, 1/2·1 is in S. Since both 1/1 and 1/2 are in S, (iii) tells us 1+1/1+2 is in S. I already have a claim, which I'm almost 100% it's true, but I need to rigorously mathematically prove it, and also, I'm not sure if there is more to the problem Claim: Set S in contained in interval [½, 1] for a/b where 0
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/2a
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? For example, by (i), 1/1 is in S. By (ii), since 1/1 is in S, 1/2·1
is in S. Since both 1/1 and 1/2 are in S, (iii) tells us 1+1/1+2 is in S.
I already have a claim, which I'm almost 100% it's true, but I need to rigorously mathematically prove it, and also, I'm not sure if there is more to the problem
Claim: Set S in contained in interval [½, 1] for a/b where 0<a≤b≤2a
Please rigorously mathematically prove this :)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
