Concept explainers
(a)
To find: The supremum and infimum of the given set.
(a)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
be 0 and the supremum will be 1.
Hence, both infimum and supremum exist.
(b)
To find: The supremum and infimum of the given set.
(b)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
The given set is decreasing,
be 1 and the supremum will be 2.
Hence, both infimum and supremum exist.
(c)
To find: The supremum and infimum of the given set.
(c)
Answer to Problem 3E
Infimum exists and supremum doesn’t exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Therefore, the set has no upper bound and the lower bound is 0. Therefore, the infimum will
be 0 and no supremum exists.
Hence, infimum exists and supremum doesn’t exist.
(d)
To find: The supremum and infimum of the given set.
(d)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum exist.
(e)
To find: The supremum and infimum of the given set.
(e)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum exist.
(f)
To find: The supremum and infimum of the given set.
(f)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum exists.
(g)
To find: The supremum and infimum of the given set.
(g)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum exist.
(h)
To find: The supremum and infimum of the given set.
(h)
Answer to Problem 3E
Both infimum and supremum exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum exist.
(i)
To find: The supremum and infimum of the given set.
(i)
Answer to Problem 3E
Infimum exist but supremum doesn’t exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, infimum exist but supremum doesn’t exist.
(j)
To find: The supremum and infimum of the given set.
(j)
Answer to Problem 3E
Both infimum and supremum doesn’t exist.
Explanation of Solution
Given Information:
The given set is
The set that is given is
Hence, both infimum and supremum doesn’t exist.
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