In mathematics, particularly in order theory, an upper bound or majorant of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S. Dually, a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S. A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.
_q.jpg)
>>>PUT SHARE BUTTONS HERE<<<
In this Dossier
Upper and lower bounds in the context of Terminus ante quem
A terminus post quem ('limit after which', sometimes abbreviated TPQ) and terminus ante quem ('limit before which', abbreviated TAQ) specify the known limits of dating for events or items.
A terminus post quem is the earliest date the event may have happened or the item was in existence, and a terminus ante quem is the latest. An event may well have both a terminus post quem and a terminus ante quem, in which case the limits of the possible range of dates are known at both ends, but many events have just one or the other. Similarly, a terminus ad quem 'limit to which' is the latest possible date of a non-punctual event (period, era, etc.), whereas a terminus a quo 'limit from which' is the earliest. The concepts are similar to those of upper and lower bounds in mathematics.
Upper and lower bounds in the context of Supremum
The infimum is, in a precise sense, dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration. However, the general definitions remain valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered.