Infimum and supremum

The infimum of a set is its greatest lower bound, and its supremum is its least upper bound. Either may lie outside the set.

Partial order: A reflexive, antisymmetric, transitive relation that orders some or all pairs of elements. Infima and suprema are defined relative to an order, which need not compare every pair.
Greatest lower bound property: The property that every nonempty real set bounded below has an infimum in the real numbers. It ensures the infimum exists even when the set has no minimum.
Limit superior and limit inferior: The supremum and infimum limits of the tails of a sequence. They apply supremum and infimum repeatedly to capture a sequence's limiting extremes.
Infinitum: A philosophical and mathematical term for the infinite or an unbounded quantity. An infimum is a precise bound, not infinity itself.
Lower bound: An element less than or equal to every member of a specified set. An infimum is the greatest element among a set's lower bounds.
Least upper bound property: The property that every nonempty real set bounded above has a supremum in the real numbers. It ensures the supremum exists even when the set has no maximum.
Essential supremum: The least almost-everywhere upper bound of a measurable function. It adapts the supremum to ignore exceptional sets of measure zero.
Maximum: An element of a set that is greater than or equal to every other member. A supremum need not be a maximum because it may not belong to the set.
Upper bound: An element greater than or equal to every member of a specified set. A supremum is the least element among a set's upper bounds.
Maximum and minimum: The greatest and least elements of a set, when those elements belong to the set. A maximum is a supremum attained in the set; a minimum is an attained infimum.

Linked from 2 pages

Riemann integralRelated: They define the upper and lower sums used to test integrability.