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10 Mar 2023
Question 5. (15 marks) Consider the set of all real numbers r such that
-00 < r ≤ -1.
(a) Is this set bounded?
(b) Give two different upper bounds.
(c) Find the supremum of this set.
Justify your answers.![](data:image/jpeg;base64,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Question 5. (15 marks) Consider the set of all real numbers r such that
-00 < r ≤ -1.
(a) Is this set bounded?
(b) Give two different upper bounds.
(c) Find the supremum of this set.
Justify your answers.
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celluarsolLv10
10 Mar 2023
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astrodabberLv10
10 Mar 2023
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12 Mar 2023
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