joshuamcevoy said:Homework Equations
(n-2sqrt(n)) n is element of natural numbers
The supremum, also known as the least upper bound, is the smallest number that is greater than or equal to all elements in a set. The maximum, on the other hand, is the largest number in a set. In some cases, the supremum and maximum may be the same value, but this is not always the case.
Similar to the supremum and maximum, the infimum and minimum have subtle differences. The infimum, or greatest lower bound, is the largest number that is less than or equal to all elements in a set. The minimum, on the other hand, is the smallest number in a set. Again, they may be the same value in some cases, but not always.
To find the supremum and infimum of a set, you first need to list out all the elements in the set. Then, you can compare them and determine the largest and smallest values. The supremum will be the smallest value that is greater than or equal to all elements, and the infimum will be the largest value that is less than or equal to all elements.
Yes, it is possible for a set to have no supremum or infimum. This occurs when the set is unbounded, meaning there is no upper or lower limit. For example, the set of all positive numbers has no infimum, as there is no largest number that is less than or equal to all elements in the set.
Finding the supremum and infimum of a set is important in mathematical analysis and optimization problems. It allows us to define upper and lower bounds for a set, which can help us determine the behavior and limits of a function or system. It also helps us identify the maximum and minimum values within a set, which can be useful in decision making and problem solving.