Consider the following argument. Let S be a pairwise disjoint set of open intervals in R (possibly infinitely many). Since Q is dense in R (Theorem 1.2.4), each interval J belonging to the set S contains a rational number, say q♬. The function sending J to gj is a bijection from S to a subset of the countable set Q. Since every subset of a countable set is countable (bottom of page 17, Section 0.3), the set S is countable. True or false: This argument solves Exercise 1.4.7. True False

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the following argument.
Let S be a pairwise disjoint set of open intervals in R (possibly infinitely
many). Since Q is dense in R (Theorem 1.2.4), each interval J belonging to
the set S contains a rational number, say q. The function sending J to gj
is a bijection from S to a subset of the countable set Q. Since every
subset of a countable set is countable (bottom of page 17, Section 0.3),
the set S is countable.
True or false: This argument solves Exercise 1.4.7.
True
False
Transcribed Image Text:Consider the following argument. Let S be a pairwise disjoint set of open intervals in R (possibly infinitely many). Since Q is dense in R (Theorem 1.2.4), each interval J belonging to the set S contains a rational number, say q. The function sending J to gj is a bijection from S to a subset of the countable set Q. Since every subset of a countable set is countable (bottom of page 17, Section 0.3), the set S is countable. True or false: This argument solves Exercise 1.4.7. True False
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