Mathematics Exam > Mathematics Questions > If S is a set of real numbers which is bounde...
Start Learning for Free
If S is a set of real numbers which is bounded above, then Sup S is
- a)a point of closure to S
- b)not a point of closure to S
- c)prime number
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If S is a set of real numbers which is bounded above, then Sup S isa)a...
Explanation:
To understand why option A is the correct answer, let's first define the terms involved in the question.
Definition of a bounded set:
A set of real numbers S is said to be bounded above if there exists a real number M such that every element in S is less than or equal to M. In other words, there is an upper bound on the set S.
Definition of the supremum:
The supremum of a set S, denoted as Sup S, is the least upper bound of the set S. It is the smallest real number M such that every element in S is less than or equal to M.
Now, let's consider the given options one by one:
Option A: Sup S is a point of closure to S
This option is correct. The supremum of a set S is a point of closure to S because it is the smallest real number that is greater than or equal to all the elements in S. In other words, it is a point that is close to all the elements in S.
Option B: Sup S is not a point of closure to S
This option is incorrect. As explained above, the supremum of a set S is a point of closure to S.
Option C: Prime number
This option is incorrect. The supremum of a set of real numbers has nothing to do with prime numbers. It is a concept related to the bounds of a set.
Option D: None of the above
This option is incorrect. Option A is the correct answer.
Conclusion:
The supremum of a bounded set of real numbers is a point of closure to the set. It is the smallest real number that is greater than or equal to all the elements in the set.
To understand why option A is the correct answer, let's first define the terms involved in the question.
Definition of a bounded set:
A set of real numbers S is said to be bounded above if there exists a real number M such that every element in S is less than or equal to M. In other words, there is an upper bound on the set S.
Definition of the supremum:
The supremum of a set S, denoted as Sup S, is the least upper bound of the set S. It is the smallest real number M such that every element in S is less than or equal to M.
Now, let's consider the given options one by one:
Option A: Sup S is a point of closure to S
This option is correct. The supremum of a set S is a point of closure to S because it is the smallest real number that is greater than or equal to all the elements in S. In other words, it is a point that is close to all the elements in S.
Option B: Sup S is not a point of closure to S
This option is incorrect. As explained above, the supremum of a set S is a point of closure to S.
Option C: Prime number
This option is incorrect. The supremum of a set of real numbers has nothing to do with prime numbers. It is a concept related to the bounds of a set.
Option D: None of the above
This option is incorrect. Option A is the correct answer.
Conclusion:
The supremum of a bounded set of real numbers is a point of closure to the set. It is the smallest real number that is greater than or equal to all the elements in the set.
Free Test
FREE
| Start Free Test |
Community Answer
If S is a set of real numbers which is bounded above, then Sup S isa)a...
Bcas,SupS is set of all upper bound .
so it has limit points
therefore it is closed.
a smallest closed set containing S. is called closure of S
so option A is right
so it has limit points
therefore it is closed.
a smallest closed set containing S. is called closure of S
so option A is right
|
Explore Courses for Mathematics exam
|
|
If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
Question Description
If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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 If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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 If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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 If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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 If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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 If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If S is a set of real numbers which is bounded above, then Sup S isa)a point of closure to Sb)not a point of closure to Sc)prime numberd)None of the aboveCorrect 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup