the supremum is also referred to as the least upper bound (or LUB). The infimum is in a precise sense dual to the concept of a supremum. Infima and suprema...

concepts of essential infimum and essential supremum are related to the notions of infimum and supremum, but adapted to measure theory and functional analysis...

for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively. In general, when there are...

is equivalent to the existence of the infimum and supremum (proof below), the convergence of Cauchy sequences and the Bolzano–Weierstrass theorem. This...

concepts are the lower and upper Darboux sums. These are similar to Riemann sums, but the tags are replaced by the infimum and supremum (respectively) of f...

limit infimum and limit supremum of a set sequence always exist and can be used to determine convergence: the limit exists if the limit infimum and limit...

usual derivative at t. The functions are defined in terms of the infimum and supremum in order to make the Dini derivatives as "bullet proof" as possible...

an important role in PCF theory. Greatest element and least element Infimum and supremum Maximal and minimal elements Schaefer, Helmut H.; Wolff, Manfred...

lattice, with infimum and supremum symbolized by ∧ {\displaystyle \wedge } and ∨ {\displaystyle \vee } , respectively. Its universe and least element...

directed supremum. Dually, if S {\displaystyle S} is a downward directed set, then its meet (if it exists) is a directed meet or directed infimum. Let A...