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Upper Bounds, Lower Bounds, Supremum, Infimum, Bounded and Unbounded Set Video Lecture - IIT JAM
FAQs on Upper Bounds, Lower Bounds, Supremum, Infimum, Bounded and Unbounded Set Video Lecture - IIT JAM
| 1. What is an upper bound in the context of sets? |  |
Ans. In the context of sets, an upper bound is an element that is greater than or equal to all the elements of the set. It serves as an upper limit for the values in the set.
| 2. How is a lower bound defined for a set? | |
Ans. A lower bound for a set is an element that is less than or equal to all the elements of the set. It acts as a lower limit for the values in the set.
| 3. What is the supremum of a set? | |
Ans. The supremum of a set is the smallest upper bound for the set, or it can be defined as the least upper bound. It is denoted by sup(S) and must satisfy two conditions: (1) It is an upper bound for the set, and (2) It is smaller than or equal to any other upper bound of the set.
| 4. Can a set have multiple upper bounds? | |
Ans. Yes, a set can have multiple upper bounds. If an element is greater than or equal to all the elements of the set, it will be considered as an upper bound. Therefore, there can be several elements that satisfy this condition and act as upper bounds.
| 5. What does it mean for a set to be bounded? | |
Ans. A set is said to be bounded if it has both an upper bound and a lower bound. This means that there are elements in the set that are greater than or equal to all other elements (upper bound) and there are elements that are less than or equal to all other elements (lower bound). If a set lacks either an upper bound or a lower bound, it is considered unbounded.
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