9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is defined to be 1 An = {x | (\n)(x € A₁)} Give an example of a family of intervals A, n=1,2,..., such that A+1 CA, for all n and A=0. Prove that your example has the stated property. G Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 10. Give an example of a family of intervals A, n=1,2,..., such that A+1 CA, for all 1 and 4 consists of a single real number. Prove that your example has the stated property. n=1 G
9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is defined to be 1 An = {x | (\n)(x € A₁)} Give an example of a family of intervals A, n=1,2,..., such that A+1 CA, for all n and A=0. Prove that your example has the stated property. G Your answer needs to be a little bit longer. Write a few sentences to complete your assignment. 10. Give an example of a family of intervals A, n=1,2,..., such that A+1 CA, for all 1 and 4 consists of a single real number. Prove that your example has the stated property. n=1 G
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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Pls. answer these two questions by typing not by handwriting.
Transcribed Image Text:9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is defined to be 1 A₂ = {x| (vn)(x €
A₁)} Give an example of a family of intervals An, n = 1,2,..., such that An+1 C An for all n and 1 An = 0). 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.
G
10. Give an example of a family of intervals A, n=1,2,..., such that An+1 CA, for all n and 4 consists of a single real number.
Prove that your example has the stated property.
n=1
Your answer needs to be a little bit longer. Write a few sentences to complete your assignment.
G
Expert Solution
Answer of question number 9.
Let An : = [ n ,) where n = 1,2, 3 ..... . So { An } n is an example of infinite collection of intervals of real line .
For next example , let consider An = [ n , ) , n = 1,2,3..... .
Here A1 A2 A3 ........... An An+1 ..... .
Suppose x An , then x [ n , ) . So n x and also n+1 x .
and it going on as n . So there is nothing to common . So x does not exists .
As defined the intersection in the question , so here An = .
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