x_{1} is an eventual extremal bound/asymptote (one sense)/limsup (limit superior/limit supremum)/liminf (limit inferior/limit infimum) of x_{2} (set, or ordered pair of a sequence or a function as the first term and the dummy variable (/input (slot)) thereof being considered as the (sometimes elidable) second term) in direction x_{3} (li) in ordered structure x_{4}.

Many of the notes of trajmaumce apply to this word with minor appropriate edits. Dependence on x_{4} is slightly less delicate than it is for "trajmaumce"; the ordering is the most important information yielded by any input of x_{4}.
If x_{2} is not a set, make sure to state (in the definition of x_{2}) the (dummy) variable of x_{2} against which this so-called "limit" is being taken.