mecraizmana'u lujvo

x1 (number) is the supremum of set x2 under (partial) ordering x3

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.

In notes:

nacyzmarai
x1 (number) is the greatest element/maximum of the set (of numbers) x2 under (partial) ordering x3
zmaraimecna'u
x1 (number) is the infimum of set x2 under (partial) ordering x3
trajmaumce
x1 (li) is an extremal bound (supremum/infimum/possibly-unattained extremum (loose sense in English)/asymptote (one sense)/best possible bound (one sense)) on set x2 (set) in direction x3 (li) in ordered structure x4; x1 bounds x2 tightly/maximally-strongly from the x3 side in x4; x2 is bounded from the x3 side by x1 and any other bound on that side is worse than is x1.