Asymptotical, a mathematical term referring to a curve approaching a line without touching it, has a few synonyms including limit, endpoint, approach, and proximity. Limit refers to the value of a function or sequence that is approached but never reached. Endpoint denotes the point in an interval at which a curve approaches but never touches. Approach refers to the process of getting closer and closer to a line or curve. Finally, proximity signifies the closeness or nearness of a curve to a line, regardless of whether they touch or intersect. Each of these synonyms can be used in place of asymptotical depending on the context and mathematical scenario.