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Supremum and Infimum

Definition: The supremum of f is the smallest upper bound of f:

sup(f) := such S:
   S is upper bound of f /\ 
   (forall S': S' is upper bound of f => S <= S').

The infimum of f is the greatest lower bound of f:

inf(f) := such I:
   I is lower bound of f /\ 
   (forall I': I' is lower bound of f => I >= I').

Author: Wolfgang Schreiner
Last Modification: December 14, 1999

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