In mathematics, the supremum of a subset of a partially ordered set is the least element of the set that is greater than or equal to every element of the subset, when such an element exists; when it exists, the supremum is unique, and any upper bound of the subset is greater than or equal to it, so the supremum is also called the least upper bound. Its counterpart, the infimum, is the greatest element that is less than or equal to every element of a subset, and is correspondingly called the greatest lower bound. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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1. Supremum (Wikipedia)
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In mathematics, the infimum (abbreviated inf; pl.: infima) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the greatest element in P {\displaystyle P} that is less than or equal to each element of S , {\displaystyle S,} if such an element exists.
Infimum and supremum (Wikipedia)
In Branch: Analysis, Lead paragraphQuote, In Branch: Analysis, Lead paragraph
Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration.
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