Page "Infimum" Paragraph 4

In analysis the infimum or greatest lower bound of a subset S of real numbers is denoted by inf ( S ) and is defined to be the biggest real number that is smaller than or equal to every number in S. If no such number exists ( because S is not bounded below ), then we define inf ( S ) = −∞.

If S is empty, we define inf ( S ) = ∞ ( see extended real number line ).