Infimum/Supremum| Definition, Numerical form and Real world Analogy

• The infimum (inf) of a set is the greatest lower bound; it is the largest number that is less than or equal to every number in the set.
• The supremum (sup) of a set is the least upper bound; it is the smallest number that is greater than or equal to every number in the set.

Real World Analogy

• Think of a set of numbers as a collection of values on a line.
• The infimum is like the lowest point on the line that is still above all the values.
• The supremum is like the highest point on the line that is still below all the values.

Real Life Examples

1. Temperature Setting:
   • Consider a thermostat adjusting the room temperature.
   • The infimum might represent the lowest comfortable temperature.
   • The supremum might represent the highest comfortable temperature.
2. Exam Scores:
   • In a class, the infimum could be the lowest score anyone achieved.
   • The supremum could be the highest score anyone achieved.