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The closed interval S = [0, 1] is
- a)bounded above
- b)unbounded below
- c)unbounded above
- d)no maximal element
Correct answer is option 'A'. Can you explain this answer?
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The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unb...
The Closed Interval [0, 1]
Introduction:
The closed interval [0, 1] is a subset of the real number line and includes all real numbers between 0 and 1, including the endpoints 0 and 1. In this explanation, we will determine whether the interval is bounded above, bounded below, unbounded above, or has no maximal element.
Bounded Above:
To determine if the closed interval [0, 1] is bounded above, we need to check if there is a real number that is greater than or equal to every element in the interval. In this case, the number 1 is greater than or equal to every element in the interval, as 1 is the upper bound of the interval. Therefore, the closed interval [0, 1] is bounded above.
Unbounded Below:
To determine if the closed interval [0, 1] is unbounded below, we need to check if there is a real number that is less than or equal to every element in the interval. In this case, the number 0 is less than or equal to every element in the interval, as 0 is the lower bound of the interval. Therefore, the closed interval [0, 1] is unbounded below.
Unbounded Above:
To determine if the closed interval [0, 1] is unbounded above, we need to check if there is no real number that is greater than or equal to every element in the interval. However, as mentioned earlier, the number 1 is greater than or equal to every element in the interval, acting as the upper bound. Therefore, the closed interval [0, 1] is not unbounded above.
No Maximal Element:
A maximal element in a set is an element that is greater than or equal to every other element in the set. In the closed interval [0, 1], there is no maximal element because no element in the interval is greater than or equal to every other element. The upper bound of the interval, which is 1, is greater than all the other elements in the interval, but it is not greater than or equal to itself. Therefore, the closed interval [0, 1] has no maximal element.
Conclusion:
In summary, the closed interval [0, 1] is bounded above by the number 1, unbounded below, not unbounded above, and has no maximal element.
Introduction:
The closed interval [0, 1] is a subset of the real number line and includes all real numbers between 0 and 1, including the endpoints 0 and 1. In this explanation, we will determine whether the interval is bounded above, bounded below, unbounded above, or has no maximal element.
Bounded Above:
To determine if the closed interval [0, 1] is bounded above, we need to check if there is a real number that is greater than or equal to every element in the interval. In this case, the number 1 is greater than or equal to every element in the interval, as 1 is the upper bound of the interval. Therefore, the closed interval [0, 1] is bounded above.
Unbounded Below:
To determine if the closed interval [0, 1] is unbounded below, we need to check if there is a real number that is less than or equal to every element in the interval. In this case, the number 0 is less than or equal to every element in the interval, as 0 is the lower bound of the interval. Therefore, the closed interval [0, 1] is unbounded below.
Unbounded Above:
To determine if the closed interval [0, 1] is unbounded above, we need to check if there is no real number that is greater than or equal to every element in the interval. However, as mentioned earlier, the number 1 is greater than or equal to every element in the interval, acting as the upper bound. Therefore, the closed interval [0, 1] is not unbounded above.
No Maximal Element:
A maximal element in a set is an element that is greater than or equal to every other element in the set. In the closed interval [0, 1], there is no maximal element because no element in the interval is greater than or equal to every other element. The upper bound of the interval, which is 1, is greater than all the other elements in the interval, but it is not greater than or equal to itself. Therefore, the closed interval [0, 1] has no maximal element.
Conclusion:
In summary, the closed interval [0, 1] is bounded above by the number 1, unbounded below, not unbounded above, and has no maximal element.
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The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unb...
This is set is bounded above by 1 because all elements of [0,1] are less than equal to 1
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The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unbounded aboved)no maximal elementCorrect answer is option 'A'. Can you explain this answer?
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The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unbounded aboved)no maximal elementCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unbounded aboved)no maximal elementCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The closed interval S = [0, 1] isa)bounded aboveb)unbounded belowc)unbounded aboved)no maximal elementCorrect answer is option 'A'. Can you explain this answer?.
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