The supremum of a set is the smallest number that is greater than or equal to all of the elements in the set. It is also referred to as the least upper bound.
The supremum is the smallest number that is greater than or equal to all of the elements in a set, while the maximum is the largest element in the set. The supremum may or may not be an actual element in the set, whereas the maximum will always be an element in the set.
Yes, the supremum can be equal to infinity if the set has no upper bound. In this case, the supremum is considered to be the limit of the set as it approaches infinity.
The concept of supremum is used in various mathematical fields, such as calculus, real analysis, and topology. It is used to define important concepts like continuity, convergence, and compactness.
An example of finding the supremum of a set is finding the supremum of the set of real numbers less than 1. In this case, the supremum would be 1, as it is the smallest number that is greater than or equal to all the elements in the set.