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Exercise 1.4.5 (Hard): Construct an explicit bijection from [0, 1] to (0,1).

Exercise 1.4.5 (Hard): Construct an explicit bijection from [0, 1] to (0,1).

Advanced Engineering Mathematics
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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Please solve exercise 1.4.5 with detailed explanations 

Exercise 1.4.4 (Hard): Construct an explicit bijection from (0, 1] to (0,1). Hint: One approach is as follows: First map (1/2, 1] to (0,1/2], then map (1/4, 1/2] to (1/2, 3/4], etc. Write down the map explicitly, that is, write down an algorithm that tells you exactly what number goes where. Then prove that the map is a bijection. Exercise 1.4.5 (Hard): Construct an explicit bijection from [0, 1] to (0, 1).
Transcribed Image Text:Exercise 1.4.4 (Hard): Construct an explicit bijection from (0, 1] to (0,1). Hint: One approach is as follows: First map (1/2, 1] to (0,1/2], then map (1/4, 1/2] to (1/2, 3/4], etc. Write down the map explicitly, that is, write down an algorithm that tells you exactly what number goes where. Then prove that the map is a bijection. Exercise 1.4.5 (Hard): Construct an explicit bijection from [0, 1] to (0, 1).
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Explicit bijection between the interval 0,1 and the interval 0,1.

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