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Given a non-empty subset S of R (real number) on the interval [0, 5]. Then, any numbers greater than 5 is an upper bound of S since it is greater than all of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bounds of S. Among all these upper bound, the one with the smallest value is known as the _______ of S. 
  • a)
    Supremum 
  • b)
    Minimum
  • c)
    Infimum 
  • d)
    Maximum
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Given a non-empty subset S of R (real number) on the interval [0, 5]. ...
The supremum of a set of numbers defined on an interval is also known as the least upper bound, lub. On the contrary, the infimum of a set of numbers is also known as the greatest lower bound, glb.
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Most Upvoted Answer
Given a non-empty subset S of R (real number) on the interval [0, 5]. ...
Explanation:

Definition of Upper Bound:
An upper bound of a set S is a number that is greater than or equal to every element in S.

Given Information:
We are given a non-empty subset S of real numbers on the interval [0, 5].

Identifying Upper Bounds:
To determine the upper bounds of S, we need to find numbers that are greater than or equal to every element in S. Since S is a subset of the interval [0, 5], any number greater than 5 will be greater than all the numbers in S. Therefore, any number greater than 5 is an upper bound of S.

List of Upper Bounds:
Based on the given information, we can identify the following upper bounds of S:
- 5.01
- 5.1
- 6
- 7

Definition of Supremum:
The supremum of a set S, denoted by sup(S), is the smallest upper bound of S. In other words, it is the least upper bound of S.

Finding the Supremum:
Among all the upper bounds listed above, we need to find the one with the smallest value. This will be the supremum of S.

Choosing the Supremum:
Comparing the upper bounds, we can see that 5.01 is the smallest value among them. Therefore, the supremum of S is 5.01.

Answer:
The correct answer is option A) Supremum. The supremum of S is the smallest upper bound of S, which in this case is 5.01.
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Community Answer
Given a non-empty subset S of R (real number) on the interval [0, 5]. ...
Supremum is defined as the least value from the set of all the upper bounds. here supremum will be 5

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Given a non-empty subset S of R (real number) on the interval [0, 5]. Then, any numbers greater than 5 is an upper bound of S since it is greater than all of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bounds of S. Among all these upper bound, the one with the smallest value is known as the _______ of S.a)Supremumb)Minimumc)Infimumd)MaximumCorrect answer is option 'A'. Can you explain this answer?
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Given a non-empty subset S of R (real number) on the interval [0, 5]. Then, any numbers greater than 5 is an upper bound of S since it is greater than all of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bounds of S. Among all these upper bound, the one with the smallest value is known as the _______ of S.a)Supremumb)Minimumc)Infimumd)MaximumCorrect 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 Given a non-empty subset S of R (real number) on the interval [0, 5]. Then, any numbers greater than 5 is an upper bound of S since it is greater than all of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bounds of S. Among all these upper bound, the one with the smallest value is known as the _______ of S.a)Supremumb)Minimumc)Infimumd)MaximumCorrect 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 Given a non-empty subset S of R (real number) on the interval [0, 5]. Then, any numbers greater than 5 is an upper bound of S since it is greater than all of the numbers contained in S. Therefore, we can say that 5.01, 5.1, 6 and 7 are all upper bounds of S. Among all these upper bound, the one with the smallest value is known as the _______ of S.a)Supremumb)Minimumc)Infimumd)MaximumCorrect answer is option 'A'. Can you explain this answer?.
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