What is a supremum or least upper bound?

The supremum, or least upper bound, of a set is the smallest value that is greater than or equal to every element in that set. It may or may not be an element of the set itself. For example, the supremum of the set of all real numbers less than 2 is 2, even though 2 is not included in the set. The concept is crucial in mathematical analysis and helps in understanding limits and convergence.