Upper Lower Bounds Quiz Form
Test your understanding of upper and lower bounds in mathematics. Complete all questions below.
What is the definition of an upper bound for a set of real numbers?
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Select the correct statement about lower bounds.
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A lower bound is any number less than or equal to all elements of the set.
A lower bound is any number greater than all elements of the set.
A lower bound must be an element of the set.
Other
Calculate the least upper bound (supremum) of the set S = {x ∈ ℝ : x < 3}.
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Which of the following sets has a greatest lower bound (infimum) of 0?
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S = {x ∈ ℝ : x > 0}
S = {x ∈ ℝ : x ≥ 0}
S = {x ∈ ℝ : x < 0}
Other
Provide an example of a set with no upper bound.
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For the set S = {1/n : n ∈ ℕ}, what is the greatest lower bound (infimum)?
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Choose the correct upper bound for the set S = {x ∈ ℝ : x ≤ 7}.
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Please Select
7
8
6
Other
Explain the difference between a maximum and an upper bound.
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Fill in the blank: The least upper bound of a set is also called the
Answer
.
Is every upper bound of a set also a maximum? Explain briefly.
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