r the closed interval In that each I, contains In+1. Is it true that there exists an element that belongs to each and I,? [an, b,]. Yes, because the Nested Interval Property guarantees this. Yes, because there is always an element common to all sets. No, because the intersection of an infinte amount of sets is alwyas empty. No, because this would be saying that there's an element common to all sets, which is false.
r the closed interval In that each I, contains In+1. Is it true that there exists an element that belongs to each and I,? [an, b,]. Yes, because the Nested Interval Property guarantees this. Yes, because there is always an element common to all sets. No, because the intersection of an infinte amount of sets is alwyas empty. No, because this would be saying that there's an element common to all sets, which is false.
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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![r the closed interval In
[an, b,].
that each I, contains I,41. Is it true that there exists an element that belongs to each and I,?
n+1 •
Yes, because the Nested Interval Property guarantees this.
Yes, because there is always an element common to all sets.
No, because the intersection of an infinte amount of sets is alwyas empty.
No, because this would be saying that there's an element common to all sets, which is false.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bd9bd0-40fd-4172-a50a-abb52eb6a8c1%2F0c9b40fe-eaad-465e-ad8d-456a6522f71f%2F4lfi5pn_processed.png&w=3840&q=75)
Transcribed Image Text:r the closed interval In
[an, b,].
that each I, contains I,41. Is it true that there exists an element that belongs to each and I,?
n+1 •
Yes, because the Nested Interval Property guarantees this.
Yes, because there is always an element common to all sets.
No, because the intersection of an infinte amount of sets is alwyas empty.
No, because this would be saying that there's an element common to all sets, which is false.
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