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Let (Ai)i∈I a family of superiorly bounded subsets of R. and we say that for every i∈I, si=sup(Ai), fi=inf(Ai).  Let K be the set: K={1/n-2/m+5/p; where n,m,p ∈ N*} A. Are the sets A=Ui∈I(Ai) and B=∩i∈I(Ai) bounded superiorly? If Ai⊆[0,100] B. What are the values of sup(A) and inf (A)? C. What are the values of sup(B) and inf (B)? D. What are the values of sup(K) and inf (K)?

Let (Ai)i∈I a family of superiorly bounded subsets of R. and we say that for every i∈I, si=sup(Ai), fi=inf(Ai).  Let K be the set: K={1/n-2/m+5/p; where n,m,p ∈ N*} A. Are the sets A=Ui∈I(Ai) and B=∩i∈I(Ai) bounded superiorly? If Ai⊆[0,100] B. What are the values of sup(A) and inf (A)? C. What are the values of sup(B) and inf (B)? D. What are the values of sup(K) and inf (K)?

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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Let (Ai)i∈I a family of superiorly bounded subsets of R. and we say that for every i∈I, si=sup(Ai), fi=inf(Ai). 

Let K be the set: K={1/n-2/m+5/p; where n,m,p ∈ N*}

A. Are the sets A=Ui∈I(Ai) and B=∩i∈I(Ai) bounded superiorly?

If Ai⊆[0,100]

B. What are the values of sup(A) and inf (A)?

C. What are the values of sup(B) and inf (B)?

D. What are the values of sup(K) and inf (K)?

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