Mathematics Exam > Mathematics Questions > The closed interval S = [0, 1] isa)bounded ab...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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.
Free Test
FREE
| Start Free Test |
Community Answer
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
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
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?
Question Description
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?.
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup