nacyzmarai
lujvo x_{1} (number) is the greatest element/maximum of the set (of numbers) x_{2} under (partial) ordering x_{3} x1 must be a set. If this word is being used as a function (max), common but lazy mathematical practice allows for speaking of "the maximum of a function" (including sequences) or to constrain the maximum with respect to certain variables, but these constraints can and properly ought to be incorporated into the definition of the set of which the maximum is being taken. This word is not limited to purely mathematical usage and the set can be defined loosely (such as in "the maximum number of people whom I permit to be invited" wherein the set x2 is understood to be the set of the possible acceptable numbers of guests allowed by the speaker). The maximum x1 must belong to set x2; compare with: mecraizmana'u (supremum). See also: nacmecrai.


mecraizmana'u
lujvo x_{1} (number) is the supremum of set x_{2} under (partial) ordering x_{3} x2 must be a set; although it is standard (and lazy) mathematical practice to speak of "the supremum of a function" (including sequences) in some domain or to constrain the supremum with respect to certain variables in some way, all of these features can and ought to be constraints defining the set of which the supremum is taken; in Lojban, no leeway is given toward such sloppiness. See also: zmaraimecna'u, nacyzmarai.


nacmecrai
lujvo x_{1} (number) is the least element/minimum of the set (of numbers) x_{2} under (partial) ordering x_{3} x1 must be a set. If this word is being used as a function (min), common but lazy mathematical practice allows for speaking of "the minimum of a function" (including sequences) or to constrain the minimum with respect to certain variables, but these constraints can and properly ought to be incorporated into the definition of the set of which the minimum is being taken. This word is not limited to purely mathematical usage and the set can be defined loosely (such as in "the minimum legally acceptable wage" wherein the set x2 is understood to be the set of all legally acceptable wages). The minimum x1 must belong to set x2; compare with: zmaraimecna'u (infimum). See also: nacyzmarai.
