Is Supremum and Infimum?

A set is bounded if it is bounded both from above and below. The supremum of a set is its least upper bound and the infimum is its greatest upper bound.

Is infimum the same as supremum?

Yes, one point sets have the same supremum and infimum (actually the same maximum and minimum).

Are Supremum and Infimum unique?

Similarly, since b is a least upper bound and a an upper bound of S, b ≤ a. Thus a = b, showing that the supremum of a set is unique. Intuitively, another way of stating the definition of supremum is that no number smaller than the supremum can be an upper bound of the given set.