x1 is an eventual extremal bound/asymptote (one sense)/limsup (limit superior/limit supremum)/liminf (limit inferior/limit infimum) of x2 (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 x3 (li) in ordered structure x4.
Many of the notes of trajmaumce apply to this word with minor appropriate edits. Dependence on x4 is slightly less delicate than it is for "trajmaumce"; the ordering is the most important information yielded by any input of x4. If x2 is not a set, make sure to state (in the definition of x2) the (dummy) variable of x2 against which this so-called "limit" is being taken.