Let (S,≼) be a linearly ordered set with the Least-Upper-Bound Property. Let A and B be non-empty and bounded below subsets of S. (i) Prove that A ∪ B is bounded below in S. (ii) Prove that inf(A ∪ B) ≼ inf(A) by using the definition of the infimum of a set in S.
Let (S,≼) be a linearly ordered set with the Least-Upper-Bound Property. Let A and B be non-empty and bounded below subsets of S. (i) Prove that A ∪ B is bounded below in S. (ii) Prove that inf(A ∪ B) ≼ inf(A) by using the definition of the infimum of a set in S.
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 (S,≼) be a linearly ordered set with the Least-Upper-Bound Property. Let A and B be non-empty and bounded below subsets of S.
(i) Prove that A ∪ B is bounded below in S.
(ii) Prove that inf(A ∪ B) ≼ inf(A) by using the definition of the infimum of a set in S.
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