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4. Professor Doofus mistakenly writes the following: Let a be an upper bound for a set A. Then: a = sup A if and only if there exists 8 >0 and a € A such that a-8

4. Professor Doofus mistakenly writes the following: Let a be an upper bound for a set A. Then: a = sup A if and only if there exists 8 >0 and a € A such that a-8

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 4TFE: Label each of the following statements as either true or false. Every upper bound of a nonempty set...
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4. Professor Doofus mistakenly writes the following: Let a be an upper bound for a set A. Then: a = sup A if and only if there exists 8 >0 and a € A such that a-8 <a. Give an example which shows that Doofus' statement is incorrect.
Transcribed Image Text:4. Professor Doofus mistakenly writes the following: Let a be an upper bound for a set A. Then: a = sup A if and only if there exists 8 >0 and a € A such that a-8 <a. Give an example which shows that Doofus' statement is incorrect.
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