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The infimum and supremum of the set A=[0,4) are, respectively*1 point0 and null4 and null0 and 4null and 4

Question

The infimum and supremum of the set A = [0, 4) are, respectively:

  • 0 and 4
  • 0 and null
  • 4 and null
  • null and 4
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Solution

The infimum and supremum of the set A=[0,4) are, respectively, 0 and 4.

Here's why:

  1. The infimum (or greatest lower bound) of a set is the largest number that is less than or equal to all numbers in the set. In this case, the infimum of the set A=[0,4) is 0 because 0 is included in the set and there is no number in the set that is less than 0.

  2. The supremum (or least upper bound) of a set is the smallest number that is greater than or equal to all numbers in the set. In this case, the supremum of the set A=[0,4) is 4 because even though 4 is not included in the set, there is no number in the set that is greater than 4.

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