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2.6.2(1) Let A CR be a non – empty set. Refer to Example 2.5.13 for the definition of a greatest element of a set; the definition and properties of a least element of a set are completely analogous. (1)Prove that if a € A is a greatest element of A, then A has a least upper bound and lubA = a.

2.6.2(1) Let A CR be a non – empty set. Refer to Example 2.5.13 for the definition of a greatest element of a set; the definition and properties of a least element of a set are completely analogous. (1)Prove that if a € A is a greatest element of A, then A has a least upper bound and lubA = a.

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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2.6.2(1)

Please include a formal proof. 

2.6.2(1) Let A CR be a non – empty set. Refer to Example 2.5.13 for the definition of a greatest element of a set; the definition and properties of a least element of a set are completely analogous. (1)Prove that if a € A is a greatest element of A, then A has a least upper bound and lubA = a.
Transcribed Image Text:2.6.2(1) Let A CR be a non – empty set. Refer to Example 2.5.13 for the definition of a greatest element of a set; the definition and properties of a least element of a set are completely analogous. (1)Prove that if a € A is a greatest element of A, then A has a least upper bound and lubA = a.
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