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?
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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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?
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