Infimum and supremum

In mathematics, the infimum or greatest lower bound of a set "A", written as formula_1, is the greatest element among all lower bounds of "A". Similarly, the supremum or least upper bound of "A", written as formula_2, is the smallest element among all upper bounds of "A".
For example, if "A" is the set formula_3, then formula_4 and formula_5. Infimum and supremum are unique, if they exist. Infimum and supremum are key concepts in the field of mathematical analysis.