Let A be a set of real numbers such that infla1a2a₁, a2 € A a₁ # a2} > 0. Prove that every Cauchy sequence of elements in A converges to a point of A.
Let A be a set of real numbers such that infla1a2a₁, a2 € A a₁ # a2} > 0. Prove that every Cauchy sequence of elements in A converges to a point of A.
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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Question 4 in the attached image.
![3. Let f : [2,3] → {1,3} be a continuous function such that the equation f (x) – x = 0 has a solution a
in [2,3]. What can you say about the function f?
4. Let A be a set of real numbers such that
inf{|a1 – a2| : a1, a2 € A a1 7 a2} > 0.
Prove that every Cauchy sequence of elements in A converges to a point of A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60376414-a2ea-43c4-9458-9e08e3951006%2F44748c8e-5ac3-4e3e-942d-e3068d227b70%2Fwaymxj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let f : [2,3] → {1,3} be a continuous function such that the equation f (x) – x = 0 has a solution a
in [2,3]. What can you say about the function f?
4. Let A be a set of real numbers such that
inf{|a1 – a2| : a1, a2 € A a1 7 a2} > 0.
Prove that every Cauchy sequence of elements in A converges to a point of A.
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