9. Given an infinite collection An, n = 1, 2, ... of intervals of the real line, their intersection is defined to be N=₁ A₂ = {x| (\n)(x = A₁)} Give an example of a family of intervals A₁, n = 1, 2, ..., such that An+1 C An for all n and 0. Prove that your example has the stated property. 1 An = Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. n=1 10. Give an example of a family of intervals A₁, n = 1,2,..., such that An+1 C An for all n and 1 An consists of a single real number. Prove that your example has the stated property. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
9. Given an infinite collection An, n = 1, 2, ... of intervals of the real line, their intersection is defined to be N=₁ A₂ = {x| (\n)(x = A₁)} Give an example of a family of intervals A₁, n = 1, 2, ..., such that An+1 C An for all n and 0. Prove that your example has the stated property. 1 An = Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. n=1 10. Give an example of a family of intervals A₁, n = 1,2,..., such that An+1 C An for all n and 1 An consists of a single real number. Prove that your example has the stated property. Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
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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Transcribed Image Text:9. Given an infinite collection An, n = 1, 2, ... of intervals of the real line, their intersection is defined to be
N=₁ A₂ = {x| (\n)(x = A₁)} Give an example of a family of intervals A₁, n = 1, 2, ..., such that An+1 C An
for all n and
0. Prove that your example has the stated property.
1 An
=
Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
n=1
10. Give an example of a family of intervals A₁, n = 1,2,..., such that An+1 C An for all n and 1 An consists
of a single real number. Prove that your example has the stated property.
Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
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