Prove that a lower bound of a set might not be unique but the infimum of a given set is unique. Attempt: Consider some E⊂R such that E≠∅. E is bounded below ⟺∃m∈Rsuch thata≥m∀a∈E.

Is the supremum unique?

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. ... The supremum or infimum of a set A is unique if it exists.

Can the infimum be infinity?

The infimum and supremum are the best possible lower and upper bounds of a set. They need not be real numbers; they can be ±∞ for unbounded sets.