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Unformatted text preview: a A . This shows that- is an upper bound for-A . Suppose - . If- is to be the least upper bound for-A , we must show that there exists an element-a -A with-a . If - , then- . Since is the greatest lower bound for A , it follows that- is not a lower bound for A . Thus, there exists an a A with a - . I.e.,-a . Since-a -A when a A , this completes the proof. 1...
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This note was uploaded on 07/15/2010 for the course MATH 521 taught by Professor Metcalfe during the Spring '10 term at University of North Carolina Wilmington.
- Spring '10