Definition of Infimum (Greatest Lower Bound)

Let A be a subset of the set of all real numbers ℝ. A real number c is called the infinum of A (c = inf A) if satisfies:

• c is a lower bound of A i.e. for every x ∈ A, x ≥ c, and
• if d is a lower bound of A then c ≥ d.