The example of a close subset A of R − Q such that A ⊆ [ 3 , 4 ] of A is not compact.

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Answer 1

Question

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

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Answer 2

Question

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

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Answer 3

Question

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

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Answer 4

Question

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

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Answer 5

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

Answer 6

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

Answer 7

Chapter 7.5, Problem 5E

(a)

To determine

To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

Answer 8

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

Answer 9

(b)

To determine

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

Answer 10

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

Answer 11

(c)

To determine

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

The example of a close subset A of R − Q such that A ⊆ [ 3 , 4 ] of A is not compact.

Solution Summary: The author explains that R-Q is a set of irrational number.

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To Find: The example of a close subset A of R−Q such that A⊆[3,4] of A is not compact.

To Find: The example of a bounded infinite subset of R−Q∩[3,4] that has no accumulation point in R−Q .

To Find: The example of a bounded increasing sequence x of irrational number such that {xn:n∈N}⊆[3,4] and x has no limit in R−Q .

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Chapter 7 Solutions