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infimum
This term is used exclusively within the specialized register of mathematical analysis and set theory. It describes a precise boundary condition where a value serves as the absolute ceiling for all possible lower bounds of a given set. While it is often synonymous with the minimum in casual conversation, it differs technically because an infimum does not need to be a member of the set itself.
In professional mathematical discourse, the term is frequently paired with its counterpart, the supremum. Using these terms instead of minimum or maximum signals a rigorous approach to limits and completeness, particularly when dealing with open intervals where a true minimum may not exist.
Meanings
Examples
The infimum of the set of positive real numbers is zero.
We need to prove that the infimum is actually attained as a minimum.
The infimum of the sequence is the limit as n approaches infinity.
I wonder if the infimum of this function exists on an open interval.
The infimum is the greatest lower bound of the given set.
Let us define the infimum of the set S as the value L.
The infimum of an empty set is defined as positive infinity.